Patent Publication Number: US-2007097390-A1

Title: Method for correcting cartridge color shifts for performing imaging with an imaging apparatus using a cartridge

Description:
CROSS REFERENCES TO RELATED APPLICATIONS  
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     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT  
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     REFERENCE TO SEQUENTIAL LISTING, ETC.  
      None.  
     BACKGROUND  
      1. Field of the Invention  
      The present invention relates generally to imaging, and more particularly to a method for correcting cartridge color shifts for performing imaging with an imaging apparatus using a cartridge.  
      2. Description of the Related Art  
      Current imaging systems typically employ one or more replaceable cartridges of different types that are used to disperse a colorant on a print medium. For example, an ink jet printer may employ a CMY cartridge that prints full strength cyan, magenta, and yellow inks, and may also employ a Kcm cartridge that prints full strength black, dilute cyan, and dilute magenta inks.  
      The color shift between one cartridge and another is a common problem in color reproduction. When an imaging system reproduces colors using colorants from more than one type of cartridge, the reproduced color variations will be more complicated than using a single cartridge. For example, in an imaging system that uses a color cartridge with CMY inks (cyan, magenta, and yellow) and photo cartridge with Kcm inks (black, diluted cyan, and diluted magenta), called CMYKcm imaging system, the output color variation depends not only on the CMY cartridge color shifts but also on the Kcm cartridge color shifts. Correcting the composite color variations is more challenging than single cartridge color correction.  
     SUMMARY OF THE INVENTION  
      The invention, in one exemplary embodiment, relates to a method for correcting cartridge color shifts for performing imaging with an imaging apparatus using a cartridge, the cartridge having a plurality of colorants. The method includes determining a spectral signature band for each colorant of the plurality of colorants to yield a plurality of spectral signature bands; determining a minimum number of the spectral signature bands from the plurality of spectral signature bands to form a group of spectral signature bands that are applicable to all colorants of the plurality of colorants; determining a primary colorant profile for each colorant of the plurality of colorants of the cartridge based on the minimum number of the spectral signature bands; determining primary colorant shift data based on the primary colorant profile for each colorant and based on a standard cartridge primary colorant profile; estimating combined colorant shift data using the primary colorant shift data; and generating color correction data based on the combined colorant shift data for use in imaging with an imaging apparatus using the cartridge.  
      The invention, in another exemplary embodiment, relates to a method for correcting cartridge color shifts for performing imaging with an imaging apparatus using a cartridge, the cartridge having a plurality of colorants. The method includes determining spectral signature data for each colorant of the plurality of colorants; selecting a spectral signature band common to all of the plurality of colorants; determining primary colorant shift data within the spectral signature band for the cartridge based on a standard cartridge primary colorant profile and based on the spectral signature band; and generating color correction data based on the primary colorant shift data for printing with an imaging apparatus using the cartridge.  
      The invention, in another exemplary embodiment, relates to a method for correcting cartridge color shifts for performing imaging with an imaging apparatus using a cartridge, the cartridge having a plurality of colorants. The method includes selecting a minimum spectral signature band common to all of the plurality of colorants; printing a test image for each colorant of the plurality of colorants individually using a varying amount of the colorant coverage values within a range of colorant coverage values for each colorant; measuring from the test image only a single reflectance value for each colorant coverage value of the varying amount of coverage values of the test image within the spectral signature band; determining primary colorant shift data based on the spectral signature band for the cartridge and based on a standard cartridge primary colorant profile and based on the measuring; and generating color correction data based on the primary colorant shift data for printing with an imaging apparatus using the cartridge. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
      The above-mentioned and other features and advantages of this invention, and the manner of attaining them, will become more apparent and the invention will be better understood by reference to the following description of embodiments of the invention taken in conjunction with the accompanying drawings, wherein:  
       FIG. 1  is a diagrammatic depiction of an imaging system that utilizes the present invention;  
       FIG. 2  is a diagrammatic depiction of a colorspace converter accessing a composite color conversion lookup table in accordance with the present invention;  
       FIG. 3  is a flowchart that depicts method steps according to an embodiment of the present invention; and  
       FIGS. 4A-4C  depict spectral distributions of yellow, magenta, and cyan inks, respectively, with different ink coverage on plain paper. 
    
    
     DETAILED DESCRIPTION  
      It is to be understood that the invention is not limited in its application to the details of construction and the arrangement of components set forth in the following description or illustrated in the drawings. The invention is capable of other embodiments and of being practiced or of being carried out in various ways. Also, it is to be understood that the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. The use of “including,” “comprising,” or “having” and variations thereof herein is meant to encompass the items listed thereafter and equivalents thereof as well as additional items. Unless limited otherwise, the terms “connected,” “coupled,” and “mounted,” and variations thereof herein are used broadly and encompass direct and indirect connections, couplings, and mountings. In addition, the terms “connected” and “coupled” and variations thereof are not restricted to physical or mechanical connections or couplings.  
      In addition, it should be understood that embodiments of the invention include both hardware and electronic components or modules that, for purposes of discussion, may be illustrated and described as if the majority of the components were implemented solely in hardware. However, one of ordinary skill in the art, and based on a reading of this detailed description, would recognize that, in at least one embodiment, the electronic based aspects of the invention may be implemented in software. As such, it should be noted that a plurality of hardware and software-based devices, as well as a plurality of different structural components may be utilized to implement the invention. Furthermore, and as described in subsequent paragraphs, the specific mechanical configurations illustrated in the drawings are intended to exemplify embodiments of the invention and that other alternative mechanical configurations are possible.  
      Referring now to the drawings, and particularly to  FIG. 1 , there is shown a diagrammatic depiction of an imaging system  10  embodying the present invention. In the embodiment depicted, imaging system  10  includes an imaging apparatus  12  and a host  14 . Imaging apparatus  12  communicates with host  14  via a communications link  16 . Alternatively, it is contemplated that imaging system  10  may be an imaging apparatus without a corresponding host computer, such as imaging apparatus  12  in the form of a stand-alone imaging apparatus, wherein the necessary functions of host  14  are performed by imaging apparatus  12  itself.  
      Imaging apparatus  12  may be, for example, an ink jet printer and/or copier, an electrophotographic printer and/or copier, or an all-in-one (AIO) unit that includes a printer, a scanner, and possibly a fax unit. Imaging apparatus  12  includes a controller  18 , a print engine  20 , one or more printing cartridges, such as a cartridge  22  having a cartridge memory  23  and a cartridge  24  having a cartridge memory  25 , a user interface  26 , and a sensor  27 . Sensor  27  may be employed for measuring spectral data, such as reflectance data, for use in correcting cartridge color shifts in conjunction with the present invention.  
      Controller  18  is communicatively coupled to print engine  20 . Print engine  20  is configured to mount cartridge  22  and cartridge  24 , as well as to provide a communicative interface between controller  18 , and cartridge memory  23  and cartridge memory  25 . Imaging apparatus  12  has access to a network  28 , for example, such as the Internet, via a communication line  30 , and is capable of interfacing with other systems, such as an offsite computer  32  having an offsite memory  34 , in order to transmit and/or receive data for use in carrying out its imaging functions. In the present embodiment, offsite computer  32  is a network server operated by, for example, a manufacturer, distributor and/or retailer of cartridge  22 , cartridge  24 , imaging apparatus  12 , and/or imaging system  10 .  
      Controller  18  includes a processor unit and an associated memory  36 , and may be formed as one or more Application Specific Integrated Circuits (ASIC). Controller  18  may be a printer controller, a scanner controller, or may be a combined printer and scanner controller. Although controller  18  is depicted in imaging apparatus  12 , alternatively, it is contemplated that all or a portion of controller  18  may reside in host  14 . Controller  18  communicates with print engine  20 , cartridge  22  and cartridge memory  23 , and cartridge  24  and cartridge memory  25  via a communications link  38 , and with user interface  26  via a communications link  42 . Controller  18  serves to process print data, to operate print engine  20  during printing, and to perform color correction in accordance with the present invention.  
      In the context of the examples for imaging apparatus  12  given above, print engine  20  may be, for example, a color ink jet print engine or a color electrophotographic print engine, configured for forming an image on a substrate  44 , which may be one of many types of print media, such as a sheet of plain paper, fabric, photo paper, coated ink jet paper, greeting card stock, transparency stock for use with overhead projectors, iron-on transfer material for use in transferring an image to an article of clothing, and back-lit film for use in creating advertisement displays and the like. As an ink jet print engine, print engine  20  operates cartridge  22  and cartridge  24  to eject ink droplets onto substrate  44  in order to reproduce text or images, etc. As an electrophotographic print engine, print engine  20  causes cartridge  22  and cartridge  24  to deposit toner onto substrate  44 , which is then fused to substrate  44  by a fuser (not shown).  
      Host  14  may be, for example, a personal computer, including memory  46 , an input device  48 , such as a keyboard, and a display monitor  50 . A peripheral device  52 , such as a digital camera, is coupled to host  14  via a communication link  54 . Host  14  further includes a processor, input/output (I/O) interfaces, and is connected to network  28  via a communication line  56 , and hence, has access to offsite computer  32 , including offsite memory  34 . Memory  46  may be any or all of RAM, ROM, NVRAM, or any available type of computer memory, and may include one or more of a mass data storage device, such as a floppy drive, a hard drive, a CD and/or a DVD unit or other optical storage devices.  
      During operation, host  14  includes in its memory  46  a software program including program instructions that function as an imaging driver  58 , e.g., printer/scanner driver software, for imaging apparatus  12 . Imaging driver  58  is in communication with controller  18  of imaging apparatus  12  via communications link  16 . Imaging driver  58  facilitates communication between imaging apparatus  12  and host  14 , and provides formatted print data to imaging apparatus  12 , and more particularly, to print engine  20 . Although imaging driver  58  is disclosed as residing in memory  46  of host  14 , it is contemplated that, alternatively, all or a portion of imaging driver  58  may be located in controller  18  of imaging apparatus  12 . Although controller  18  is used to perform color correction in accordance with the present invention, it is alternatively contemplated that all or a portion of the color correction may be performed by imaging driver  58 .  
      Referring now to  FIG. 2 , imaging driver  58  includes a colorspace converter  60 . Although described herein as residing in imaging driver  58 , colorspace converter  60  may be in the form of firmware or software, and may reside in either imaging driver  58  or controller  18 . Alternatively, some portions of colorspace converter  60  may reside in imaging driver  58 , while other portions reside in controller  18 .  
      Colorspace converter  60  is used for converting color signals from a first colorspace, such as an RGB colorspace employed by display monitor  50  or a scanner, to a second colorspace, for example, CMYK (cyan, magenta, yellow, and black), which is used by print engine  20 . The output of colorspace converter  60  may be used to provide multilevel printing, for example, CcMmYyKcm printing, which employs the following ink drop sizes/strengths/compositions: large undiluted cyan dye-based ink drops (“C”), small undiluted cyan dye-based drops (“c”), large undiluted magenta dye-based drops (“M”), small undiluted magenta dye-based ink drops (“m”), large undiluted yellow dye-based ink drops (“Y”), small undiluted yellow dye-based ink drops (“y”), undiluted black pigment-based ink drops (“K”), dilute cyan pigment-based ink drops (second occurrence in “CcMmYyKcm” of “c”), and dilute magenta pigment-based ink drops (second occurrence of “m”).  
      It will be understood that any reference to CMYK may include any combination of the CcMmYyKcm inks, and that any reference to CMY may include any combination of CcMmYy inks. For convenience, however, the present embodiment is described with respect to 6-level CMYKcm printing, wherein, for example, cartridge  22  is a CMY cartridge, and cartridge  24  is a Kcm photo cartridge.  
      Coupled to colorspace converter  60  are a standard color conversion lookup table  62  and a color correction data lookup table  64 , which together define a composite color conversion lookup table  66 . Standard color conversion lookup table  62  and composite color conversion lookup table  66  are multidimensional lookup tables having at least three dimensions, and include RGB values and CMYKcm values, wherein each CMYKcm output value corresponds to an RGB input value. Standard color conversion lookup table  62  and composite color conversion lookup table  66  may also include other data, such as spectral data, or other values or parameters for use in performing color conversion or color correction.  
      Standard color conversion lookup table  62  is the basic color conversion lookup table accessed by colorspace converter  60  of imaging apparatus  12  and imaging system  10  for performing color conversion. Color correction data lookup table  64  is specifically associated with the present invention method, forming an inventive component of the composite color conversion lookup table  66  used in the color conversion and color correction processes. Color correction data lookup table  64  includes color correction data that when employed in conjunction with standard color conversion lookup table  62 , for example, as part of composite color conversion lookup table  66 , provides color shift corrected color conversion data as output from colorspace converter  60 . As shown in  FIG. 2 , for example, colorspace converter  60  converts input RBG color data for a displayed or scanned image into color shift corrected CMYKcm output data that may be printed by print engine  20  using composite color conversion lookup table  66 , hence using color correction data lookup table  64  and standard color conversion lookup table  62 .  
      Standard color conversion lookup table  62  incorporates color conversion data to support color conversion via composite color conversion lookup table  66  for multiple color formats and the multiple types of substrate  44 . Color formats supported by standard color conversion lookup table  62  and color correction data lookup table  64 , hence composite color conversion lookup table  66 , include, for example, monochrome K output using true black ink only, CMYcm color output, wherein neutral colors are formed using process black, also known as composite black, produced by using a combination of CMYcm color inks, and CMYKcm color printing using a combination of full strength and dilute color inks and true black ink.  
      Color correction data lookup table  64  is a multidimensional lookup table having at least three dimensions that includes multidimensional color data for cartridge  22  and cartridge  24  expressed in a device independent CIELAB colorspace form. Alternatively, color correction data lookup table  64  may be in the form of multidimensional CIEXYZ device-independent colorspace data. However, the multidimensional color data of color correction data lookup table  64  may be expressed in any convenient device-dependent or device-independent colorspace. It will be understood that color correction data lookup table  64  may also include other data, such as spectral data, or other values or parameters for use in performing color conversion or color calibration.  
      Color correction data lookup table  64  is determined based on various data stored in a memory accessible by imaging apparatus  12 . The data from which color correction data lookup table  64  is determined includes the “signature” colors of cartridge  22  and cartridge  24 , such as, for example, the individual color output characteristics of the particular cartridge  22  and the particular cartridge  24  employed in imaging apparatus  12 . The signature colors are determined based on spectral data as set forth in the following embodiments of the present invention.  
      The signature colors of a cartridge are a small set of colors that may be used to characterize the cartridge, or to classify the cartridge into a class of cartridges with similar color characteristics. In the present embodiment, signature color data for cartridge  22  and cartridge  24  are stored in a memory accessible by imaging apparatus  12 , for example, cartridge memory  23  and cartridge memory  25 , and read into memory  36  of controller  18 , or, alternatively, read into the memory storing imaging driver  58 . Alternatively, it is contemplated that the signature color data for cartridge  22  and cartridge  24  may be stored in offsite memory  34  of offsite computer  32 , and retrieved by imaging system  10 , e.g., by imaging apparatus  12  and/or host  14 , and stored into memory  36  of controller  18 , or, alternatively, the memory storing imaging driver  58 .  
      In the embodiment described herein, the colorant increment data is arranged in color correction data lookup table  64  in an ordered format for access by colorspace converter  60 , wherein the order of the data allows colorspace converter  60  to correlate the data of color correction data lookup table  64  with the similarly ordered data of standard color conversion lookup table  62  in defining composite color conversion lookup table  66 .  
      Each of standard color conversion lookup table  62 , color correction data lookup table  64  and composite color conversion lookup table  66  may alternatively be in the form of groups of polynomial functions capable of providing the same multidimensional output as if in the form of lookup tables.  
      The color shift from one cartridge to another is a common problem in color reproduction. In order to correct the color shift, the following method may be proposed: (a) measure cartridge signature colors on a first substrate (inexpensive substrate like plain paper) including combinations of different inks in the cartridge on the manufacturing line, and storing the signature color data in a first memory (e.g., cartridge memory). The signature color is expressed by
 
ξ=ƒ(φ)  (Equation 1)
 
 where ξ is the CIELAB tri-color (L*, a*, b*) where L* is lightness, a* redness-greenness, and b* yellowness-blueness, φ represents the colorant in the cartridge (e.g., φ=(C,M,Y) for a cartridge containing cyan, magenta, and yellow inks), ƒ denotes that ξ is a function of φ implemented as a lookup table or a group of polynomial functions. The next step would be (b) storing the signature color of a standard cartridge on the first substrate in a second memory (e.g., printer driver/firmware), which is expressed by
 
ξ s =ƒ s (φ)  (Equation 2)
 
 where subscript s denotes “standard cartridge.” Following, step (c) would include storing the signature color of the standard cartridge on a second substrate (e.g., glossy paper) in the second memory, which is expressed by
 
ξ sp =ƒ sp (φ)  (Equation 3)
 
 where subscript p denotes “paper being used by the user”. Finally, step (d) would include building on-line a color correction table based on Equations 1-3. An important part of the above method is obtaining cartridge signature colors on the manufacturing line (Equation 1). 
 
      It is desirable to simplify the above process and reduce the cost in obtaining cartridge signature colors on the manufacturing line. Thus, in accordance with the present invention, a method in which only color patches of individual inks (no ink combinations) are printed and only a single value (not tri-stimulus values, such as CIELAB data) for each color s patch is measured on the manufacturing line. This may reduce printing time, measuring time, data storage size, instrumentation expense, labor cost, and total cost. Additionally, the present invention may be applied onboard for individual printers, and thereby eliminate the process on the manufacturing line.  
      As set forth below, the present invention provides a method for measuring and correcting cartridge color shifts, including determining a minimum number of spectral signature bands for all individual colorants, e.g., inks, measuring a single value for each color patch based on the spectral signature band, determining primary colorant shift matrix, and estimating combined colorant shift matrix for color correction.  
      Referring now to  FIG. 3 , steps S 100 -S 110  generally describe a method for correcting cartridge color shifts for performing imaging with an imaging apparatus, such as imaging apparatus  12 , using a cartridge such as cartridge  22  and/or cartridge  24 , each cartridge having a plurality of colorants, e.g., inks. Although the present embodiment is described with respect to two different cartridges, those skilled in the art would appreciate that the present invention is suited to the use of any number of cartridges, one or more, each having any number of colorants.  
      At step S 100 , a spectral signature band for each colorant of the plurality of colorants in cartridge  22  and cartridge  24  is determined, yielding a plurality of spectral signature bands, and the minimum number of spectral signature bands that form a group of spectral signature bands that is applicable to all colorants is determined. Preferably, the number of spectral signature bands that form the group is less than the total number of spectral signature bands, but the group has sufficient bandwidth to capture wavelengths from all of the colorants within an acceptable variation in relative magnitude of reflectance.  
      Step S 100  includes printing a test image for each colorant (e.g., ink) individually, i.e., not a combination of inks. The test image is printed with a varying amount of colorant coverage values within a range of colorant coverage values for each ink, e.g., from 0 to 100% ink coverage. In the present embodiment, the test image is a plurality of color test patches, e.g., color patches, each of the plurality of test patches pertaining to a different colorant coverage value of the varying amount of colorant coverage values for each colorant, e.g., pertaining to a different ink coverage value in the range of 0 to 100% for the present embodiment.  
      A spectral signature band of a colorant is defined as a portion, e.g., bandwidth, of the spectral distribution in the visible electromagnetic spectrum of the ink under which the area changes significantly with a variation in the ink coverage on a substrate. Stated differently, a spectral signature band is selected as a bandwidth of wavelengths in the visible electromagnetic spectrum having an optimal variation in relative magnitude of reflectance for a corresponding range of colorant coverage values for each colorant of the cartridge. A variation in relative magnitude of reflectance is a change in reflectance corresponding with a change in colorant coverage, e.g., colorant coverage values ranging from 0% ink coverage to 100% ink coverage on a printed sheet. An optimal variation in relative magnitude of reflectance is a predetermined variation in magnitude of reflectance that is readily measured within the capability of the instrument used to measure reflectance, e.g., sensor  27 . In the present embodiment, for example, the optimal variation in relative magnitude of reflectance is approximately 50. However, it will be understood that the present invention is not limited to a particular predetermined variation in magnitude of reflectance, but rather, the predetermined variation in magnitude of reflectance may be any value suitable for use in the imaging apparatus, for example, based on design and pricing parameters.  
      For example, referring now to  FIGS. 4A-4C , the spectral distributions of yellow, magenta, and cyan inks with different ink coverages on a plain paper are illustrated. It is seen that the yellow ink spectral distribution of  FIG. 4A  change significantly with changes in ink coverage (percentage values of coverage, e.g., 0% or paper white, 25%, 75%, and 100% ink coverage) in the band between about 400 and 500 nm (e.g., a bandwidth of about 100 nanometers located between about 400 nanometers and about 500 nanometers), but there are almost no changes in the band between about 540 nm and about 700 nm. Therefore, the band between about 400 and 500 nm is defined as spectral signature band  68  for yellow ink, having variation in relative magnitude of reflectance  69  having a magnitude of approximately 90.  
      Similarly, it is seen that the magenta ink spectral distribution of  FIG. 4B  change significantly with changes in ink coverage in the band between about 430 nm and about 600 nm (e.g., a bandwidth of about  170  nm located between about 430 nm and about 600 nm), but there are almost no changes in the band between about 600 nm and 700 nm. Thus, the band between about 430 nm and 600 nm is defined as spectral signature band  70  for magenta ink, having variation in relative magnitude of reflectance  71  having a magnitude of approximately 90.  
      In the present exemplary embodiment, spectral signature band  72  for cyan is depicted in  FIG. 4C  as being from about 425 nm to about 510 nm, and having variation in relative magnitude of reflectance  73  with a value of approximately 56, as depicted in  FIG. 4C . Although variation in relative magnitude of reflectance  73  of spectral signature band  72  for cyan is not as large as variation in relative magnitude of reflectance  69  for yellow and variation in relative magnitude of reflectance  71  for magenta, it is large enough for sufficiently accurate measurement using sensor  27 .  
      Thus, it is seen from  FIGS. 4A-4C  that at least one spectral signature band may be found for each ink. If there exists one spectral signature band that is common to all of the individual inks contained in one cartridge or multiple cartridges of a printer, only one filter, or only one light source, whose spectra are mainly within the signature band may be required for sensor  27 , which may allow the use of a lower cost sensor  27 . Depending on the spectral properties of the inks, more than one signature band may be required, i.e., if there is not a reasonable amount of bandwidth in the spectral signature bands common to all inks. But the fewer bands required, the more cost of sensor  27  may be reduced.  
      Accordingly, the following procedure may be used to determine each spectral signature band and to determine the minimum number of spectral signature bands for all individual inks under consideration.  
      (1) For each of the inks under consideration, sample n points (n=5 was found to be acceptable) ranging from 0% to 100% of ink coverage and print out a color patch for each point. The total number (N) of color patches for m inks of one cartridge will be (only one paper-white patch (0% ink) is selected):
 
 N=m ( n− 1)+1  (Equation 4)
 
      (2) Select one standard cartridge and several (5 or more) non-standard cartridges covering the normally encountered color shift range. Print out N color patches for each of these cartridges. A standard cartridge is a hypothetical cartridge representing the average output of the particular type of cartridge, e.g., standard CMY cartridge representing the average cartridge  22 , or standard Kcm cartridge representing the average cartridge  24 .  
      (3) Measure spectral data for each color patch with a spectrophotometer covering wavelength from about 400 nm to about 700 nm and sampling one point per 10 nm interval, giving 31 data points per color patch. Also, measure CIELAB (L*, a*, b*) for each color patch. Comparing the spectral data of a non-standard cartridge to that of a standard cartridge will give the colorant shift matrix. This matrix is then used to estimate the CIELAB (L*, a*, b*) for the non-standard cartridge. The difference between the estimated and measured color values will be the error. If the spectral data in a band is sensitive to the colorant change, then the error will be small. Otherwise, the error may be large.  
      (4) Select a minimum bandwidth that is easily realizable for a filter or a LED (light emitting diode).  
      (5) For a given bandwidth, the band is moved along the measuring range (about 400 nm to about 700 nm) as shown in  FIG. 4C .  
      (6) For each position of the band, error is computed using the spectral data within the given bandwidth. The error may be averaged for a group of inks. Each group may have 1, 2, . . . , and up to m inks. For example, there may be 6 groups for a CMY cartridge: C, M, Y, CM, MY, and CMY.  
      (7) Increase the bandwidth by a measuring interval (10 nm) and repeat steps 5 and 6.  
      (8) Select the minimum number of groups/bands (one group has one band that gives a minimum error when the band is moved along the measuring range), each of which has minimal or tolerable error. If several groups have a similar error, a higher priority is given to a group that has more number of inks. For the above example, if the CMY group has a band with similar error as the other groups, then it should be selected, since only one filter or one LED will be needed in sensor  27  for the 3 inks (i.e., the minimum number of spectral signature bands=1).  
      The inventors have tested pigmented cyan, magenta, and yellow inks using the above procedure, and the results are shown below in Table 1. It is seen that the CIELAB error (ΔE) ranges from 0.9 to 1.6 for the 6 groups: C, M, Y, CM, MY, and CMY. Therefore, it is feasible to use only one signature band (410-520 nm from the CMY group) that is common to the three C, M, and Y inks. This may allow a lower cost sensor  27  having a single filter/LED than a spectral sensor that employs three filters/LEDs for the three inks (one per ink).  
               TABLE 1                          CIELAB color error vs. spectral signature band                                     Signature Band           No.   Inks in a group   (nm)   Average error (ΔE)               1   C   520-560   1.3       2   M   430-550   0.9       3   Y   400-470   1.6       4   C, M   420-600   1.1       5   M, Y   400-470   1.3       6   C, M, Y   410-520   1.4                  
 
      At step S 102 , a primary colorant profile is determined for each colorant, e.g., ink, of the plurality of colorants of the cartridge or cartridges, based on the minimum number of spectral signature bands, i.e., based on determining spectral data for the test image (which are color patches in the present embodiment) within the minimum number of spectral signature bands. Determining the spectral data includes measuring only a single value for each colorant coverage value of the varying amount of colorant coverage values of the test image within the minimum number of the spectral signature bands. In the present embodiment, the single value that is measured is a reflectance value measured from each color patch using sensor  27 .  
      Once a spectral signature band for each ink is determined, a filter or LED is selected for sensor  27  based on the spectral signature bands. A broadband sensor  27  is then used to measure a single value for each color patch of the ink. The measured signal, referred to as a primary colorant profile, is expressed by:
 
y r =g(x)  (Equation 5)
 
 where y r  is the signal proportional to the reflected light of a color patch (only one ink per color patch), subscript r denotes “reflected”, x is the digital count proportional to the ink percentage (for 8-bit value, x=0 for 0% ink, and x=255 for 100% ink), and g denotes the function relationship. When conducting simulation with spectral data measured with a spectrophotometer, g(x) will be the sum of the spectral data within the signature band. 
 
      The signal of the paper-white patch (i.e., 0% ink coverage) may be given by:
 
y rw =g(0)  (Equation 6)
 
 where, subscript w denotes “white”. To remove the additive noise, the paper-white signal may be subtracted from that of the non-white color patch, giving an absorbed signal of the ink in a color patch:
 
 y   a   =g (0)− g ( x )  (Equation 7)
 
 where, subscript a denotes “absorbed”. If the noise of the paper-white patch is negligible compared to its signal (y rw ), then color patch signal may be normalized by the paper-white signal to minimize the impact of the instrument signal shifts with time due to aging, yielding:  
               y   na     =     1   -       g   ⁡     (   x   )         g   ⁡     (   0   )                   (     Equation   ⁢           ⁢   8     )             
 
 where, subscript n denotes “normalized”. 
 
      At step S 104 , primary colorant shift data is determined based on the primary colorant profile for each ink, and based on a standard cartridge primary colorant profile for each corresponding ink, set forth as follows:  
      Let Equation 7 represent the signal from a non-standard cartridge on a first substrate (inexpensive substrate like plain paper), and the signal from a standard cartridge on the same substrate be denoted by:
 
 y   sa   =g   s (0)− g   s ( x )  (Equation 9)
 
 where, subscript s denotes “standard cartridge”. The standard cartridge is determined and characterized in terms of CIELAB (L*, a*, b*) by the factory off the cartridge manufacturing line, e.g., based on average data from a plurality of cartridges. The standard cartridge signature color on the first substrate is expressed by Equation 2 and rewritten below:
 
ξ s =ƒ s (φ)  (Equation 10)
 
 which includes color values for both individual inks and their combinations. It is considered that the systematic (non-random) color shift of a non-standard cartridge may be compensated by shifting the colorant digital count (percentage of ink on the substrate). The shifted digital count is called effective colorant shift, or simply called colorant shift. If the colorant shift of a non-standard cartridge is known, then its CIELAB color shifts can be estimated using the standard cartridge signature color profile (Equation 10) by shifting the colorant variable (φ). 
 
      The following is a procedure to determine the primary colorant shifts (without ink combinations) based on the signals given in Equations 7 and 9.  
      (1) For a given primary colorant digital count x s , find y sa  in Equation 9.  
      (2) Make the left value y a  of Equation 7 equal y sa , find x using inverted computation.  
      (3) The primary colorant shift (Δx p ) that is generally changed with the colorant digital count (x) is given by:
 
Δ x   p   =x−x   s   (Equation 11)
 
 where, subscripts denotes “primary ink” without ink combinations. The same procedure is applied to each of the m inks. Then a primary colorant shift matrix may be expressed by:
 
Δφ p ={Δx p     i     }i= 0,1, . . . ,( m− 1)  (Equation 12)
 
      The primary colorant shift matrix Δφ p  plus φ s  (φ=φ s +Δφ p ) may be entered to Equation 10 to compute the estimated CIELAB color values of the non-standard cartridge primary inks.  
      To verify the accuracy of the primary colorant shift matrix, the actual CIELAB color values of the same color patches used to measure the absorption signal ya may be measured with a spectrophotometer and used to compute the CIELAB color error (ΔE) against the estimated color values. The result is shown in Table 1, above. As set forth above using one signature band (about 410 nm to about 520 nm from the CMY group) for the C, M, and Y three inks is quite acceptable since the error is small. Thus, the minimum number of spectral signature bands takes the form of one minimum signature band common to all of the colorants, e.g., that substantially encompasses but does not exceed spectral signature bands  68 ,  70 , and  72 . Accordingly, in the present embodiment, the single reflectance value measured for each color patch is measured within the one minimum signature band to yield the primary colorant profile for each ink.  
      At step S 106 , combined colorant shift data is estimated using the primary colorant shift data, set forth as follows:  
      The effective shift of a colorant is generally different when it is alone (Δx p ) than when it is combined with other colorants (Δx) due to the interaction of the diffraction and reflection between different colorants. It is assumed herein that combined colorant shift data is related to the primary colorant shift (without ink combination) in the following manner:
 
Δx=λ(Δx p ) μ   (Equation 13)
 
 where, λ and μ are variables (called ink interaction coefficients) which are theoretically the functions of the combined colorants (φ) and primary colorant shifts (Δφ p ), that is,
 
λ=ƒ λ (φ,Δφ p )  (Equation 14)
 
 and
 
μ=ƒ μ (φ,Δφ p )  (Equation 15)
 
      The procedure of estimating the ink interaction coefficients λ and μ in the present embodiment is as follows:  
      (1) For each of the inks under consideration, sample n points (n=5 was found to be acceptable) ranging from 0% to 100% of ink and print out a color patch for each point. The total number (N) of color patches for m inks of one cartridge will be calculated with Equation 4.  
      (2) Select one standard cartridge and several (15 or more) non-standard cartridges covering the normally encountered color shift range. Print out N color patches for each of these cartridges.  
      (3) Measure y a  or y sa  (Equation 7 or 9) for each patch.  
      (4) Determine primary colorant shift (Δx p ) (Equation 11) for each patch.  
      (5) For each cartridge, sample all combination points (n m ), print a color patch for each point, and measure CIELAB (L*, a*, b*) for each patch. This will yield measured color profiles for standard and non-standard cartridges (the non-standard cartridges representing those particular cartridges for which color shift correction is being performed).  
      (6) Set initial values of λ and μ for each ink at each of the n m  points (λ=μ=1.0 for points without ink combinations). Alternatively, λ and μ can be represented by polynomial functions and the coefficients can be initialized in this step.  
      (7) Compute the combined colorant shift (Δx) (Equation 13) for each ink at each of the n m  points.  
      (8) For each point, Interpolate the measured color profile of the standard cartridge with the sum of the point coordinates and the associated colorant shifts. This will give an estimated color profile for a non-standard cartridge.  
      (9) Compute and sum up the CIELAB color error between the estimated and measured color profiles of the non-standard cartridges.  
      (10) If the error reaches minimum or accepted level, output λ and μ as a lookup table or output polynomial coefficients. Otherwise, adjust parameters according to a pre-selected optimization procedure, and repeat steps 7-10.  
      With the ink interaction coefficients λ and μ determined, the combined colorant shift of each ink can be computed with Equation 13 to form a combined colorant shift matrix (Δφ) as follows:
 
Δφ={Δx 0 ,Δx 1 , . . . ,Δx m−1 }  (Equation 16)
 
      This matrix Δφ plus φ s  (φ=φ s +Δφ) may be entered to the signature color profile of the standard cartridge (Equation 2 or 10) to compute the estimated signature color profile for the non-standard cartridge as shown in Equation 1.  
      At step S 108 , color correction data, e.g., color correction data lookup table  64 , is generated based on the combined colorant shift data, for example, using equations 1-3, for use in imaging with imaging apparatus  12  using the cartridge, e.g., the particular cartridge  22  and/or cartridge  24  for which the above steps S 100 -S 106  were performed.  
      At step S 110 , standard color conversion data, e.g., standard color conversion lookup table  62 , is modified using color correction data lookup table  64  to form composite color conversion lookup table  66  for printing with imaging apparatus  12  using the particular cartridge  22  and/or cartridge  24 .  
      To verify the feasibility of the above procedure, the present inventors tested 8 different standard CMY cartridges with one standard cartridge and one base color table. In order to simulate very broad color shifts compared to the standard cartridge, additional digital count percentages are added to several cases as shown in Table 2. For example, test case  4  is added by 20% cyan, that is, the cyan digital count of any color table grid will be added by 20% within the digital count limit (enhancing cyan channel by 20%). For each test case, each ink is sampled 5 points covering the whole range, resulting in a total of 5×5×5=125 combination points. One set of 125 color values is actually measured with a spectrophotometer. Another set of 125 color values is estimated using the procedure developed in the present invention (set λ=μ=1.0, g(x) in Equation 5 is obtained using the spectral data within the signature band from about 410 nm to about 520 nm for all C, M and Y inks). The CIELAB color error (ΔE) between the two sets of data is shown in Table II, below.  
               TABLE 2                          CIELAB color error between estimated and measured data                                 Added                   colorants to a base   Average error   Average error       Non-   color table (simulating   measured with L*   measured with       standard   broad color shifts   for cyan &amp;   signature band:       cartridge   compared to standard   magenta, b* for   410-520 nm for       No.   cartridge).   yellow   all inks               1       1.5   1.4       2       1.9   2.1       3       1.6   2.5       4   C: 20%   1.8   1.9       5   M: 10%   1.8   1.9       6   Y: 15%   1.9   1.6       7   M: 10%, Y: 15%   1.5   1.7       8   C: 20%, M:   1.9   2.3           10%, Y: 15%                  
 
      To further verify the above procedure, still another set of 125 color values is each test case in such a way that each primary color patch is measured with a spectrophotometer but only a single value is selected rather than tri-values: L* is selected for cyan and magenta patches, and b* for yellow patches. That is, g(x) in Equation 5 is replaced by L* for cyan and magenta, and by b* for yellow (set λ=μ=1.0). This estimation error is also shown in Table 2.  
      It is seen in Table 2 that the errors of the two estimation methods are very close. This is because L* is sensitive to the change of cyan or magenta and b* is sensitive to the change of yellow, whereas the total spectral response within the signature band from about 410 nm to about 520 nm is sensitive to the change of cyan, magenta, or yellow. The errors are quite acceptable in practice, since the error will be further reduced when the actual values of λ and μ are determined), it is felt that the present invention will be beneficial in industrial applications.  
      The foregoing description of several methods and an embodiment of the invention has been presented for purposes of illustration. It is not intended to be exhaustive or to limit the invention to the precise steps and/or forms disclosed, and obviously many modifications and variations are possible in light of the above teaching. It is intended that the scope of the invention be defined by the claims appended hereto.