Abstract:
A method and system for the determination of toner usage in proportion to image-feature density, with independent estimation of each color toner module consumption. The system accurately accounts for image-wise color interactions due to color occlusion that may effect the actual amount of toner used by multiple color modules. The method includes a toner replenishment flow control process that responds to the toner consumption/depletion in the developer material (e.g., toner and carrier) as determined by one or more estimation modules, and thus maintains a stable and constant toner/carrier concentration ratio.

Description:
FIELD OF THE INVENTION 
     This invention relates generally to a printing method and system and, more particularly, to a method and system of performing feed-forward toner consumption estimation to manage replenishment of toners during printing. 
     BACKGROUND OF THE INVENTION 
     Maintaining stable toner concentration levels is important for maintaining image quality in a printing environment. More specifically, dispensing too little toner because of low toner concentration levels may create areas in a printed image that appear faded, while too much toner may saturate a region in a printed image. 
     In monochrome (i.e., black and white) printing environments, feedback control systems have been used to regulate toner concentration levels during printing in an attempt to maintain acceptable levels of printed image quality. Typically, these feedback control systems use sensors to measure toner concentration levels in small patches developed during inter-document zones. When the feedback indicates that the toner concentrations levels are too low to maintain an acceptable printed image quality, the toner is mixed with a carrier in the mixing sump until a desired mixture and level is reached. 
     Although these prior systems work, they have had some problems. One of the problems is the limited sampling period during the inter-document zones which does not provide adequate feedback information about toner concentration levels. As a result, toner concentration levels may actually be too low or too high, but the erroneous condition may not be corrected early enough because of the inaccurate detection and feedback. Another problem is the large lag or delay time between recognizing the need to replenish until the time the toner can be replenished to return the toner concentration level to a nominal state. In fact, in high speed printing systems, sole reliance on a feedback sensor and control system has proven to be marginally stable or unstable in maintaining toner concentration at an acceptably narrow range when many high-density images, demanding considerable toner consumption, are printed. As a result, image quality may suffer until the toner can be replenished. 
     In color xerography, maintaining stable and accurate toner concentration levels may be more imperative for achieving consistent printed image quality. Poor color balance in printed images may result if toner concentration levels are not maintained at appropriate levels during printing. Further, particularly for image-on-image (“IOI”) xerographic color printers, but not limited thereto, the adverse effects caused by improper toner concentration levels are compounded by the IOI interactions of different color separations in the printed images. 
     Thus, in high speed printing environments, for example, a need exists for metering toner in proportion to image density to anticipate toner consumption in real time to avoid the delays and errors noted above. Furthermore, obtaining a reasonably accurate signal for each color separation in a IOI color printer, for example, would require corrections for interactions between color separations. 
     SUMMARY OF THE INVENTION 
     A method for managing replenishment of toners in accordance with one embodiment of the present invention includes determining a quantity of image units for each of one or more colors in a printed image, adjusting each of the quantity of image units based upon one or more color relationships among the one or more colors, and replenishing one or more of the toners when the adjusted quantity of image units for the one or more of the toners indicates a need for replenishment. 
     A system for managing replenishment of toners in accordance with the present invention includes a quantizing system, an adjustment system, and a replenishment system. The quantizing system determines a quantity of image units for each of one or more colors in a printed image. The adjustment system adjusts each of the quantity of image units based upon one or more color relationships among the one or more colors. The replenishment system replenishes one or more of the toners when the adjusted quantity of image units for the one or more of the toners indicates a need for replenishment. 
     The present invention provides a number of advantages, including enabling the accumulation of high-definition contone image data at very high data rates and accounting for and correcting color-image interactions and image-wise occlusions during pixel estimation. In addition, the present invention enables toner concentration levels to be maintained at desired levels during color xerography while improving overall image quality. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram of a system for performing feed-forward toner consumption estimation during printing in accordance with one embodiment; 
     FIG. 2 is a block diagram of a magenta estimation module used in the system for performing feed-forward toner consumption estimation during printing; 
     FIG. 3 is a block diagram of a pixel accumulator circuit used in the magenta estimation module; 
     FIG. 4 is a block diagram of a pixel quantizing circuit used in the magenta estimation module; 
     FIG. 5 is a flowchart of a process for performing feed-forward toner consumption estimation during printing in accordance with another embodiment; and 
     FIG. 6 is a diagram showing an exemplary photoreceptor divided into contone tile regions. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     An image path system  10  for maintaining toner concentration levels during printing in accordance with one embodiment of the present invention is illustrated in FIGS. 1-4. Image path system  10  includes digital front end (“DFE”) controller  12  coupled to printer controller  13 , DFE controller interfaces  14 ( 1 )- 14 ( 4 ), therefrom to render units  16 ( 1 )- 16 ( 4 ), therefrom to raster output scanners (“ROS”) interfaces  18 ( 1 )- 18 ( 4 ), therefrom to ROS devices  20 ( 1 )- 20 ( 4 ) and to feed forward pixel count (“FFPC”) estimation modules  22 ( 1 )- 22 ( 4 ). The present invention provides a number of advantages, including enabling the accumulation of high-definition contone image data at very high data rates and accounting for and correcting color image interactions and image-wise occlusions during pixel estimation. In addition, the present invention enables toner concentration levels to be accurately maintained at desired levels during printing and improves overall image quality. 
     Referring more specifically to FIG. 1, DFE controller  12  is coupled to DFE interfaces  14 ( 1 )- 14 ( 4 ) and printer controller  13 . DFE controller  12  may include one or more processors, circuitry and memory storage devices, which may be coupled together by one or more buses to send video data to image path system  10 . In this particular embodiment, DFE controller  12  executes instructions for converting post script files representing images to be printed into contone data to be used by image path system  10 , although the image data can be received in other formats and processed in other manners by image path system  10 . The contones in this particular embodiment comprise grey scale pixels that represent one of four shades of colors: magenta; yellow; cyan; and black. In other embodiments, contones may represent other colors, such as red, green and blue. Moreover, one or more images to be printed by image path system  10  may be stored in the one or more memory storage devices in DFE controller  12 . Further, DFE controller  12  sends contone data to render units  16 ( 1 )- 16 ( 4 ), ROS interfaces  18 ( 1 )- 18 ( 4 ) and ROS devices  20 ( 1 )- 20 ( 4 ) to perform image printing while printer controller  13  maintains toner concentration levels using estimation units  22 ( 1 )- 22 ( 4 ) as described further herein. 
     Printer controller  13  is coupled to DFE controller  12 , render units  16 ( 1 )- 16 ( 4 ), ROS interfaces  18 ( 1 )- 18 ( 4 ), and FFPC estimation modules  22 ( 1 )- 22 ( 4 ). Printer controller  13  may include one or more processors, circuitry and memory storage devices, which may be coupled together by one or more buses, to control the image path system  10 . The one or more processors may execute a program of stored instructions stored in the one or more memory storage devices for controlling one or more printer devices (not illustrated) and other printing and imaging operations in image path system  10 , and for maintaining toner concentration levels during printing in accordance with the present invention as described and illustrated herein. Further, printer controller  13  maintains toner concentration levels using FFPC estimation units  22 ( 1 )- 22 ( 4 ) as described further herein. Moreover, in this particular embodiment printer controller  13  is coupled to one or more toner dispensing devices (not illustrated) to cause the toner dispensing devices to replenish one or more toner reservoirs (not illustrated) when interrupts are received by printer controller  13  from one or more FFPC estimation modules  22 ( 1 )- 22 ( 4 ), although other configurations and methods can be used to replenish toner. 
     DFE controller interfaces  14 ( 1 )- 14 ( 4 ) are coupled to render units  16 ( 1 )- 16 ( 4 ) and FFPC estimation modules  22 ( 1 )- 22 ( 4 ). DFE interfaces  14 ( 1 )- 14 ( 4 ) may include one or more processors, circuitry and memory storage devices, which may be coupled together by one or more buses, to support the high speed transfer of digital contone image data to image path system  10  with four different color image separations, including magenta, yellow, cyan, and black, for example. Moreover, DFE controller interfaces  14 ( 1 )- 14 ( 4 ) enable image data sent from DFE controller  12  to be properly formatted and synchronized upon successive transfers to render units  16 ( 1 )- 16 ( 4 ), ROS interfaces  18 ( 1 )- 18 ( 4 ), ROS devices  20 ( 1 )- 20 ( 4 ) and FFPC estimation modules  22 ( 1 )- 22 ( 4 ). 
     Render units  16 ( 1 )- 16 ( 4 ) are coupled to DFE controller interfaces  14 ( 1 )- 14 ( 4 ) and ROS interfaces  18 ( 1 )- 18 ( 4 ). Render units  16 ( 1 )- 16 ( 4 ) may include one or more processors, circuitry and memory storage devices, which may be coupled together by one or more buses to transform, for each color, contone imagewise data into halftoned binary image data on a pixel-by-pixel basis, thus presenting to ROS interfaces  18 ( 1 )- 18 ( 4 ) halftoned image patterns that will be needed to print an image representing the original image for each color separation (e.g., magenta, yellow, cyan or black). This binary halftoned image data is sent to ROS interfaces  18 ( 1 )- 18 ( 4 ), and is ultimately used by ROS devices  20 ( 1 )- 20 ( 4 ) for example, to expose a photo receptor in an image wise fashion during printing. 
     ROS interfaces  18 ( 1 )- 18 ( 4 ) are coupled to render units  16 ( 1 )- 16 ( 4 ) and ROS devices  20 ( 1 )- 20 ( 4 ). ROS interfaces  18 ( 1 )- 18 ( 4 ) may include one or more processors, circuitry and memory storage devices, which may be coupled together by one or more buses, to reformat and resynchronize image data to be used by ROS devices  20 ( 1 )- 20 ( 4 ) to write or print images stored in DFE controller  12  as modified by render units  16 ( 1 )- 16 ( 4 ). Moreover, ROS interfaces  18 ( 1 )- 18 ( 4 ) perform such functions such as turning the ROS devices  20 ( 1 )- 20 ( 4 ) on and off and providing the ROS devices  20 ( 1 )- 20 ( 4 ) with image pixel data, including pixel arrangements within a scan line and image boundaries during printing, for example. 
     ROS devices  20 ( 1 )- 20 ( 4 ) are coupled to ROS interfaces  18 ( 1 )- 18 ( 4 ). ROS devices  20 ( 1 )- 20 ( 4 ) may include one or more processors, circuitry and memory storage devices, which may be coupled together by one of more buses, to direct a laser towards a charged xerographic photoreceptor to discharge portions thereof in an imagewise pattern leaving unexposed areas charged during printing. 
     FFPC estimation modules  22 ( 1 )- 22 ( 4 ) are coupled to printer controller  13 , DFE controller interfaces  14 ( 1 )- 14 ( 4 ) and to each other by the data transfer bus  23 , which may comprise a VMEbus, PCI or Sbus type bus, for example. FFPC estimation modules  22 ( 1 )- 22 ( 4 ) each include one or more processors, circuitry and memory storage devices, which are coupled together by one or more buses, for estimating total contone counts for each of the toner colors, such as magenta, yellow, cyan, black, red, green, blue, black, gray or white, to dynamically determine toner usage during printing as described in detail further herein. 
     Referring specifically to FIG. 2, magenta FFPC estimation module  22 ( 1 ) includes RAM  24 , pixel accumulator circuit  26  and quantizer circuit  34 , which are coupled to each other by one or more buses, for analyzing and processing contone tile data received from DFE controller interfaces  14 ( 1 )- 14 ( 4 ) to generate and provide to printer controller  13  with interrupts or other signal(s) to indicate when magenta toner is needed to replenish a magenta toner reservoir for maintaining a magenta toner concentration level. 
     In this particular embodiment, RAM  24  of magenta FFPC estimation unit  22 ( 1 ) is logically organized in one or more memory sections, although other arrangements can be used. In particular, the one or more logical memory sections may include a program memory location for storing the methods described herein for estimating a total number of magenta contones, an input estimate memory location for storing contone counts obtained from one or more FFPC estimation modules  22 ( 2 )- 22 ( 4 ), an output estimate memory module for storing a magenta contone count to be used as necessary by one or more of FFPC estimation modules  22 ( 2 )- 22 ( 4 ), and a shared memory section as described further herein. Communication between RAM  24  and printer controller  13  may occur through the shared memory. Contone count estimates calculated by magenta estimation module  22 ( 1 ) are packed into the output section of RAM  24 . Furthermore, a semaphore or mailbox protocol may be constructed to send and receive command and status information. The contone count estimates packed in the output section of RAM  24  may be sent to another one or more of the FFPC estimation modules  22 ( 2 )- 22 ( 4 ). 
     Referring to FIG. 3, the pixel accumulator circuit  26  may include one or more processors, circuitry and memory storage devices, which may be coupled together by one or more buses, to count the number of magenta contones present in the image being printed. In this particular embodiment, the pixel accumulator circuit  26  includes adder circuit  28 , storages  30 ( 1 ) and  30 ( 2 ) and a selector  32 , which are coupled to each other by one or more buses. Adder circuit  28  is used for summing contone data provided to it. Storages  30 ( 1 ) and  30 ( 2 ) store an output value of adder circuit  28 , and selector  32  routes the output data from the adder circuit  28  back into adder circuit  28  so that it may be summed with additional contone data as it is received by adder circuit  28 . Although one example of a pixel accumulator circuit  26  is shown, other types of circuits or systems could be used. For example, a buffer and a digital signal microprocessor may be used to perform the function of the pixel accumulator circuit  26 . In such an embodiment, to avoid running at excessive data bandwidths, the digital signal microprocessor could be programmed to calculate a contone estimate based on every other pixel in the contone tile data. Moreover, in this example, every other pixel would be scaled by a factor of two to accommodate the pixel that was skipped. 
     Referring to FIG. 4, quantizer circuit  34  may include one or more processors, circuitry and memory storage devices, which may be coupled together by one or more buses, to apply the magenta estimation equation to the contone counts performed by pixel accumulator circuit  26 . In this particular embodiment, the one or more processors may comprise any processor suited for performing MAC operations, such as a floating point digital signal microprocessor. In particular, quantizer circuit  34  includes a multiplier unit  36 , barrel shifter  38 , estimation equation unit  42  and packer unit  44 , which are coupled to each other by one or more buses. In this embodiment, the buses may transfer 32 bits at a time, although other bus capacities can be utilized, such as 16, 64 or 128 bit capacities. Multiplier unit  36  receives magenta contone data and a magenta σ factor to convert the magenta pixel counts into an area coverage. The area coverage is the actual amount of magenta toner required to print all of the magenta contones. The σ factor is a constant that converts pixel counts into area coverage. Barrel shifter  38  quantizes the actual coverage values transmitted to it from 32 bits down to 8 bits to realize a data compression ratio of 4:1, for example, although other quantizing ratios may be used where different bus capacities are utilized. Estimation equation unit  40  applies the magenta estimation equation using the quantized results received from the barrel shifter  38  and the applied yellow and black estimation equations stored in RAM  24  as described further herein. 
     The packer unit  42  receives eight bit values for each of the contone color estimates (i.e., magenta, yellow, cyan and black) and outputs the four estimate values packed into one 32 bit value to RAM  24 , thereby reducing the overall data transfer traffic on data transfer bus  23 . Additionally, other compression techniques may be used such as Run-Length Coding, Huffman Coding, LZ, JPG or Difference, for example. Thus, a 32 bit sequence representing an estimated area of coverage for one or more contone colors may have the following structure: Emn&lt; 31 : 24 &gt;, Eyn&lt; 23 : 16 &gt;, Ecn&lt; 15 : 8 &gt; and Ekn&lt; 7 : 0 &gt;. In this example, bit locations  31 - 8  are reserved for magenta, yellow and cyan areas of coverage, respectively, while bit locations  7 - 0  are reserved for the black area of coverage. The results of the packed magenta pixel count values are provided by packer unit  46  to RAM  22 . In this particular embodiment, the quantizer circuit  26  further aides the pixel accumulator circuit  26  by retrieving intermediate contone counts (e.g., S 1 , 1 :N) from RAM  24  and loading the contone counts on the selector  32 . Further, during contone count accumulation, the packer unit  42  is instrumental in storing and retrieving contone counts for the pixel accumulator circuit  26 . 
     In this embodiment, FFPC estimation modules  22 ( 2 )- 22 ( 4 ) are the same as magenta FFPC estimation module  22 ( 1 ) described above, except with respect to their individual operation within image path system  10  as explained further herein below. 
     Referring to FIGS. 1-6, the operation of image path system  10  for performing feed-forward toner consumption estimation during printing in accordance with another embodiment of the present invention will now be described. 
     Referring to FIG. 5, beginning at step  50 , pixel accumulator  26  accumulates the number of contones in an image being printed. As images stored in DFE controller  12  are output by ROS devices  20 ( 1 )- 20 ( 4 ), the pixel information is sent to FFPC estimation modules  22 ( 1 )- 22 ( 4 ). As a photoreceptor travels through a printing mechanism (not illustrated), the photoreceptor sequentially passes under each of ROS devices  20 ( 1 )- 20 ( 4 ). In this embodiment, the photoreceptor first passes under ROS device  20 ( 1 ) (i.e., magenta), although it may first pass under any of the other ROS devices  20 ( 2 )- 20 ( 4 ). ROS device  20 ( 1 ) receives image data from ROS interface  18 ( 1 ) instructing it to direct a laser beam towards the previously charged photoreceptor, leaving it charged in an imagewise pattern at locations on the photoreceptor where the magenta toner belongs for the particular image being printed. 
     To explain a typical operation of this exemplary embodiment, the following simplified description should be considered. Referring to FIG. 6, an image  60  being printed has a quantity of X·Y pixels, where X and Y each may be any value from 0≦256, although the values may be greater or lesser. Further, image  60  is divided into one or more contone tiles  62 ( 1 )- 62 (Z). In this embodiment, image  60  may include 144 contone tiles  62 ( 1 )- 62 (Z) along the X axis, and 85 contone tiles  62 ( 1 )- 62 (Z) along the Y axis, although image  60  may include a greater or lesser number thereof. The contone tiles  62 ( 1 )- 62 (Z) in this embodiment are the same size and each include the same number of pixels. Moreover, each of contone tiles  62 ( 1 )- 62 (Z) has a quantity of N·M pixels. As the image  60  is scanned onto a photoreceptor by ROS device  20 ( 1 ), it is scanned one scan line  66 ( 1 )- 66 (Y) at a time. In this embodiment, scan lines  66 ( 1 )- 66 (Y) each comprise one row of X pixels in the image  60 , although it may comprise a greater or lesser number of pixels in other embodiments. 
     As the magenta image data for each scan line  66 ( 1 )- 66 (Y) is sent to ROS device  20 ( 1 ), it is also sent to magenta estimation module  22 ( 1 ), where it is received by adder circuit  28  in pixel accumulator circuit  26 . In particular, if pixel  64 ( 1 ) in contone tile  62 ( 1 ) includes a magenta contone, adder circuit  28  increments a magenta contone sum by the value of the contone and stores the result in storage  30 ( 1 ). As other magenta contones are detected in one or more of pixels  64 ( 2 )- 64 (N) in contone tile  62 ( 1 ), the previous contone sum value is retrieved from memory  30 ( 1 ) and is fed back into the adder circuit  28  by the selector unit  32  so that each new contone value is added to the previous sum. The pixel accumulator circuit  26  continues this process until pixel  64 (N) has been scanned. The cumulative sum for the first row of pixels (i.e.,  64 ( 1 )- 64 (N)) in contone tile  62 ( 1 ) may be expressed as S 1,1:N . 
     At this point, however, selector unit  32  does not feed the contone sum value back to adder circuit  28 , but instead outputs the value to storage  30 ( 2 ), where it is read and stored in RAM  24 . Moreover, each time N pixels within each of contone tiles  62 ( 1 )- 62 (Z) have been scanned, the contone sum value is output to storage  30 ( 2 ) and stored in RAM  24 . Pixel accumulator circuit  26  repeats the same process described above for contone tiles  62 ( 2 )- 62 ( 8 ) along the X axis of image  60  until the end of the scan line  66 ( 1 ) is reached at pixel R 1,X . 
     Adder circuit  28  eventually receives image data for the second scan line  66 ( 2 ) in contone tile  62 ( 1 ). At this point, the value of all the contones present in pixels  64 ( 1 )- 64 (n) represented as S 1,1:N  are preloaded into the selector unit  32  by the quantizer circuit  34 . The contones present in pixels  70 ( 1 )- 70 (n) are summed with the initial contone sum value S 1,1:N . The new contone sum value for contone tile  62 ( 1 ) may be represented as S 1.1:2N . The processes described above are repeated until all of the contones in contone tile  62 ( 1 ) have been scanned and summed with a final value that may be expressed as S 1,1:MN . The sum of all the contones detected in each of contone tiles  62 ( 1 )- 62 ( 8 ) along the X axis of image  60  at scan line  66 (M) is stored in RAM  24  as an array of 32-bit sums. Further, the pixel accumulator circuit  26  repeats the above described processes until all of the contones in the other contone tiles  62 ( 9 )- 62 (Z) in the image  60  have been scanned and summed. 
     Referring back to FIG. 5, at step  52 , magenta FFPC estimation module  20 ( 1 ) uses quantizer circuit  34  to apply the magenta estimation equation to compensate for color occlusions in the accumulated number of magenta contones determined in step  50  as described further herein. The quantizer circuit  34  stores partial contone counts in RAM  24 , quantizes contone tiles  62 ( 1 )- 62 (Z), applies the magenta estimation algorithm, retrieves estimate data for yellow and black contone colors stored in RAM  24 , and packs the new estimate in RAM  22  as described further herein. After scan lines  66 ( 1 )- 66 (M) in contone tile  62 ( 1 ) have been evaluated, for example, values output at storage  30 ( 2 ) are no longer passed directly to the packer unit  46 . Instead, the magenta contone count is converted to an area coverage by multiplying the sum of magenta contones in contone tile  62 ( 1 ) by an appropriate magenta σ factor as described in the estimation equations further herein below. 
     As mentioned earlier, the adverse effects caused by improper toner concentration levels are compounded by the IOI interactions of different toner colors in the printed images. With IOI xerography, successive color-plane images (e.g., magenta, yellow, cyan and black) are sequentially applied on a xerographic photoreceptor, each superimposed upon the other, where the application of each separation involves charging, exposing, and developing the image (i.e., applying toner). Thus, for each image separation applied after the first, there is occlusion, or attenuation, of the image exposure in all local areas where prior image applications were developed. Thus, for these occluded areas, less toner of the current separation is used than would be predicted by simple summation of the exposure pixels (i.e., “turned on” pixels) in the separation. 
     To aid understanding, a simple example is given, followed by more rigorous equations to predict the actual toner consumption. For example, if it were intended to produce a “mustard” color consisting of 50% black and 50% yellow blended in an image region, and black were applied first using 50% halftone screens for each statistically, half of the yellow pixels would be exposed over the black, hence occluded and not developed. Therefore, simple summation of yellow image pixels would predict almost twice the amount of yellow toner than actually consumed in the area, because no other color can develop directly over the black toner. The same problem exists for the magenta and cyan colors as well and is compounded by the fact that these toners are only partially opaque, hence producing only partial occlusion and attenuation of successively applied colors. Therefore, for example, the developability of the magenta color on the yellow color is different than the developability of the magenta color on a bare photoreceptor. Similarly, the developability of the cyan separation on the magenta separation, the cyan separation on the yellow separation, the cyan separation on the magenta separation, and the yellow separation and the cyan separation on a bare photoreceptor are all different. Hence, the CMY pixel counts can not be used directly to accurately calculate their respective toner usages. 
     Therefore, in this embodiment, magenta, yellow, cyan and black contone counts for a particular image may be denoted by m, y, c, and k respectively. Moreover, M, Y, C and K are the respective actual toner mass consumption for areas of coverage for each color contone image. In this example, σ&#39;s are constants that convert pixel counts for a contone image color into an actual average toner mass consumption per exposed pixel. The image path system  10 , using quantizer circuit  34  in estimation modules  22 ( 1 )- 22 ( 4 ), each find the values of M, Y, C, and K given m, y, c, and k values. For example, in the case where each contone color is printed separately (i.e., not using IOI printing), the pixel count is directly proportional to the actual area covered as shown below: 
     
       
           M=m*σ   m ; 
       
     
     
       
           Y=y*σ   y ; 
       
     
     
       
           C=c*σ   c ; 
       
     
     and 
     
       
           K=k*σ   k . 
       
     
     In IOI printing, however, the relationships shown above do not exist. But given m, y, c, and k, the expected value of M, Y, C and K may be calculated if the universe of all possible documents that may give rise to pixel counts of m, y, c, and k are considered, assuming that all of these documents are equally likely to give rise to such counts (i.e., that they are all distributed uniformly). Thus, for an IOI color xerographic printer, where the sequential order of color application is K, Y, M, C, for example, the expected toner mass consumption for area coverages E, per image separation, computed generally for all documents printed are: 
     
       
           E ( K ) =k*σ   k ; 
       
     
     
       
           E ( Y ) =y*σ   y   −k*y*σ   k*σ   y ; 
       
     
     
       
           E ( M ) =m*σ   m *(1 −k*σ   k ) −m*σ   m   *E ( Y )+ m*σ   m *δ my   *E ( Y ); 
       
     
     and 
     
       
           E ( C ) =c*σ   c *[1 −k*σ   k   −E ( Y ) −E ( M ) +E ( Y )* E ( M )+δ cy   *E ( Y )*(1− E ( M ))+δ cm*   E ( M )*(1 −E ( Y ))+δ cmy   *E ( Y )* E ( M )]. 
       
     
     In this example, δmy, δcy, δcm, δcmy are defined as: 
     δmy=the ratio of magenta toner developed on a yellow layer to magenta applied to bare photoreceptor; 
     δcy=the ratio of cyan toner developed on a yellow layer to cyan applied to bare photoreceptor; 
     δcm=the ratio of cyan toner developed on a magenta layer to cyan applied to bare photoreceptor; and 
     δcmy=the ratio of cyan toner developed on a magenta and yellow layer applied to bare photoreceptor. 
     Note that, for IOI color printers where the sequential order of printing color separations is different than indicated, the symbolic variables in the above specified equations may be suitably interchanged. As an example, IOI printers may print using the M, Y, C and K order mentioned above, where m, m, σ m , would be substituted in Eq. 1 above for k, k, σ k  respectively, etc. It should be noted that refinements and other modifications to these equations, reflecting more subtle interactions and nuances of the printing technology and art, may be applied, and are within the scope of the present invention. Magenta estimation module  22 ( 1 ) stores its estimation equation described above in RAM  24 , which may be accessed by estimation equation unit  40  as described herein. Thus, as contone tile data is received from accumulator circuit  26  and processed by quantizer  34  as described herein, the actual area coverage for the magenta contones in image  60  is determined by image path system  10 . 
     In this embodiment, the magenta estimation module  22 ( 1 ) cannot calculate a contone estimate and store the result in RAM  24  due to the inter-dependencies inherent in the ordered sequencing of imaging and developing the printed color toners using the IOI process as described above. In particular, the magenta estimation module  22 ( 1 ) cannot determine the actual area of coverage for magenta toner in a printed image until the yellow and black estimation equations are applied to the yellow and black contone counts and stored in RAM  24 . 
     In this embodiment, IOI interdependencies create a one image-station delay between adjacent FFPC estimation modules  22 ( 1 )- 22 ( 4 ). The relative delay between FFPC estimation modules  22 ( 1 )- 22 ( 4 ) may be expressed using W, W- 1 , W- 2 , and W- 3  to represent image, plate, page, or station, separations for magenta, yellow, cyan and black, respectively. For example, as the magenta estimation module  22 ( 1 ) calculates an estimate for image W=36, the yellow estimation  22 ( 2 ) module calculates an estimate for image W=35; the cyan estimation module  22 ( 3 ) calculates an estimate for image W=34; and the black estimation module  22 ( 4 ) calculates an estimate for image W=33. Efficient use of RAM  24  and the transfer bus  23  will accommodate communication and delay between each of FFPC estimation modules  22 ( 1 )- 22 ( 4 ). 
     Next at step  54 , magenta FFPC estimation module  22 ( 1 ) generates an interrupt if the number of magenta contones in the printed image as determined by magenta FFPC estimation module  22 ( 1 ) causes the magenta toner concentration level to reach a low level. 
     Next at step  56 , image path system  10 , by way of printer controller  13 , replenishes the magenta toner reservoir upon receiving the interrupt from magenta FFPC estimation module  22 ( 1 ). When the toner consumption estimates for the magenta FFPC estimation module  22 ( 1 ) exceeds a pre-determined threshold, the printer controller  13  is instructed by magenta FFPC module  22 ( 1 ) to add an amount of magenta toner that is comparable to the amount consumed. Printer controller  13  then causes a magenta toner dispensing device to dispense enough toner to raise the toner concentration level to an appropriate level. 
     In other embodiments of the present invention, FFPC estimation modules  22 ( 2 )- 22 ( 4 ) each perform steps  50 - 56  as described above. Moreover, one or more of FFPC estimation modules  22 ( 1 )- 22 ( 4 ) may need the estimated contone counts from one or more of FFPC estimation modules  22 ( 1 )- 22 ( 4 ). The particular order in which the determinations of the amount of toner used or remaining as well as the reliance on the estimations of one or more of these different colors in the FFPC estimation modules  22 ( 1 )- 22 ( 4 ) can vary as needed or desired for the particular application. Additionally, estimation or determination modules for other color schemes, such as for red, green, and blue could also be used. Thus, the image path system  10  containing the FFPC estimation functionality is not limited to determining contone counts and estimating their actual coverage areas in printed images for magenta, yellow, cyan or black color contones only, and is more broadly beneficial to other printers, such as monachrome, “n-colors,” xerographic, ink-jet and digital offset (i.e., lithographic) presses, for example. Moreover, the present invention, with straightforward variation of form and application, by one skilled in the art, may be generally applied for toner or ink dispensing in any of the various printing systems, technologies methods, and apparatuses mentioned above. 
     Other modifications of the present invention may occur to those skilled in the art subsequent to a review of the present application, and these modifications, including equivalents thereof, are intended to be included within the scope of the present invention. Further, the recited order of processing elements or sequences, or the use of numbers, letters, or other designations therefor, is not intended to limit the claimed processes to any order except as may be specified in the claims.