Patent Publication Number: US-2020296225-A1

Title: Image forming apparatus that uses spectral sensor

Description:
BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention relates to an image forming apparatus that uses a spectral sensor. 
     Description of the Related Art 
     There is a demand from the market to bring the print quality of an electrophotographic image forming apparatus closer to the print quality of an offset printing machine. In order to achieve this, calibration for adjusting image forming conditions depending on environmental variations or the like is required. 
     Japanese Patent Laid-Open No. 2004-086013 describes detecting a toner patch using a single spectral sensor and correcting an image forming condition based on the detection result. However, with only one sensor, the time taken for reading the toner patch becomes long. Accordingly, Japanese Patent Laid-Open No. 2016-122072 describes shortening the time taken to read the toner patch by arranging a plurality of spectral sensors and a plurality of toner patches along the main scanning direction. 
     In Japanese Patent Laid-Open No. 2016-122072, since a plurality of spectral sensors arranged in the main scanning direction are used, a technique for correcting individual differences among the plurality of spectral sensors is required. In Japanese Patent Laid-Open No. 2016-122072, it is proposed that a white background portion of a sheet is read by each spectral sensor, and individual differences are corrected based on the read results. However, even if the sheet appears uniformly as a white background to the human eye, there actually exists nonuniformity in spectral reflectance in the main scanning direction. Therefore, the Japanese Patent Laid-Open No. 2016-122072 approach may not be able to reduce the effects of sheet nonuniformities. 
     SUMMARY OF THE INVENTION 
     One of embodiments of the present invention provides an image forming apparatus comprising the following elements. A conveyance unit conveys a sheet in a first direction. An image forming unit forms an image on the sheet. A plurality of first spectral sensors measure a first measurement image formed by the image forming unit on the sheet along a second direction intersecting the first direction. A second spectral sensor measures the first measurement image formed on the sheet. A movement unit moves the second spectral sensor along a third direction intersecting the first direction. A controller determines a correction value for correcting an output value of each of the plurality of first spectral sensors, based on a measurement result of the first measurement image acquired by the plurality of first spectral sensors and a measurement result of the first measurement image acquired by the second spectral sensor while the second spectral sensor is being moved in the third direction by the movement unit, corrects, using the determined correction value, the output value output from each of the plurality of first spectral sensors by measuring a second measurement image that is formed by the image forming unit and that is for modifying an image forming condition of the image forming unit, and modifies the image forming condition based on the output value corrected by the correction unit. 
     Further features of the present invention will become apparent from the following description of exemplary embodiments (with reference to the attached drawings). 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic configuration diagram of an image forming apparatus. 
         FIG. 2  is a schematic configuration diagram of a spectral sensor. 
         FIG. 3  is a diagram illustrating a calculation unit. 
         FIG. 4  is a diagram illustrating a control system. 
         FIG. 5  is a view for showing another example of the calculation unit. 
         FIG. 6  is a view for describing an arrangement of measurement images and spectral sensors. 
         FIG. 7  is a view for describing an arrangement of measurement images and spectral sensors. 
         FIG. 8  is a flowchart for describing calibration. 
         FIG. 9  is a flowchart for describing a process for determining a correction value. 
         FIGS. 10A and 10B  are diagrams for describing correction of chromaticity. 
         FIG. 11  is a diagram illustrating a correction table. 
         FIG. 12  is a diagram for describing individual differences between spectral sensors. 
         FIG. 13  is a view for showing another example of the calculation unit. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     Hereinafter, embodiments will be described in detail with reference to the attached drawings. Note, the following embodiments are not intended to limit the scope of the claimed invention. Multiple features are described in the embodiments, but limitation is not made an invention that requires all such features, and multiple such features may be combined as appropriate. Furthermore, in the attached drawings, the same reference numerals are given to the same or similar configurations, and redundant description thereof is omitted. 
     First Embodiment 
     Image Forming Apparatus 
     As illustrated in  FIG. 1 , an image forming apparatus  100  includes a printer  101 , a reader  400 , an operation unit  180 , a buffer  141 , and a finisher  190 . The printer  101  has four stations  120 ,  121 ,  122  and  123 . Station  120  forms a yellow image. Station  121  forms a magenta image. Station  122  forms a cyan image. Station  123  forms a black image. In the following, YMCK represents yellow, magenta, cyan and black, respectively. Since each station has the same configuration, the configuration of the station  120  for forming a yellow image will be mainly described below. A photosensitive drum  105  is a photosensitive member having a photosensitive layer on its surface. A charger  111  charges the photosensitive drum  105  so that the potential of the surface of the photosensitive drum  105  becomes a predetermined potential. An exposure apparatus  103  irradiates the photosensitive drum  105  with a laser beam based on image data to form an electrostatic latent image. A developing device  112  develops the electrostatic latent image using toner to form a toner image. The developing device  112  applies a development bias to the developing sleeve to cause toner to adhere to the electrostatic latent image. 
     A primary transfer roller  118  transfers the toner image carried on the photosensitive drum  105  to an intermediate transfer belt  106 . A transfer potential for promoting transfer of the toner image is also applied to the primary transfer roller  118 . The intermediate transfer belt  106  conveys toner images formed by the stations  120 ,  121 ,  122 , and  123  to a secondary transfer position. A secondary transfer roller  114  is provided at the secondary transfer position. The secondary transfer roller  114  transfers the toner image carried on the intermediate transfer belt  106  to a sheet P conveyed from a container  113 . A transfer potential for promoting transfer of the toner image is also applied to the secondary transfer roller  114 . The sheet P on which the toner image has been transferred is conveyed to the fixing device  150 . 
     The fixing device  150  applies heat and pressure to the sheet P and the toner image to fix the toner image to the sheet P. A flapper  131  guides the sheet P to a fixing device  160  or a conveyance path  130 . The fixing device  160  is provided to increase the gloss (sheen) of the toner image formed on the sheet P or improve the fixing property of cardboard or the like. 
     A flapper  132  is a guiding member for guiding the sheet P to a conveyance path  135  or a conveyance path  139 . The conveyance path  139  conveys the sheet P to the buffer  141 . The conveyance path  135  conveys the sheet P to an inversion portion  136 . When an inversion sensor  137  provided in the conveyance path  135  detects the rear end of the sheet P, the conveyance direction of the sheet P is reversed. A flapper  133  is a guiding member for switching guidance of the sheet P to a conveyance path  138  or guidance to a conveyance path  135 . When a face down discharge mode is instructed by the user, the flapper  133  conveys the sheet P to the conveyance path  135  again. Further, the flapper  134  guides the sheet P to the conveyance path  139 . As a result, the sheet P is discharged from the image forming apparatus  100  with the printing surface of the sheet P facing downward. When a double-sided print mode is instructed by the user, the flapper  133  guides the sheet P to the conveyance path  138 . The conveyance path  138  conveys the sheet P on a first surface of which the image is formed to the secondary transfer position again. As a result, an image is also formed on a second surface of the sheet P. 
     Spectral sensors  200   a  to  200   d  for measuring the measurement image formed on the sheet P are arranged in the conveyance path  135 . Note that the alphabet characters added to the end of the reference numerals will be omitted when common matters are described. As measurement images, there are at least a measurement image used in calibration for adjusting image forming conditions, and a measurement image for correcting individual differences between the spectral sensors  200   a  to  200   d.  A measurement image generally has a plurality of test patterns. 
     The operation unit  180  includes a display device (e.g.: a liquid crystal display) and an input device (e.g.: a touch panel or hardware keys). The operation unit  180  is a user interface for accepting designation of a number of print sheets for an image and a print mode from the user. The reader  400  reads an original placed on an original platen and generates image data. 
     The buffer  141  is a post-processing device that temporarily holds the sheet P to be conveyed to the finisher  190 . The finisher  190  is a post-processing device that executes post-processing such as punching processing, stapling processing, and bookbinding processing. If the finisher  190  has not completed the post-processing of the preceding sheet P, the subsequent sheet P waits in the buffer  141 . In the present embodiment, the spectral sensor  200   e  is provided on the conveyance path in the buffer  141 . The spectral sensor  200   e  also measures an image for measurement in the same manner as the spectral sensors  200   a  to  200   d.  The measurement result of the spectral sensor  200   e  is used to correct individual differences between the spectral sensors  200   a  to  200   d.  The image forming apparatus  100  has various conveyance paths, and conveyance rollers or conveyance belts driven by motors are provided for each conveyance path. 
     Spectral Sensors 
     As illustrated in  FIG. 2 , the spectral sensor  200  includes a white LED  201 , a diffraction grating  202 , a line sensor  203 , a calculation unit  204 , and a memory  205 . The white LED  201  illuminates the measurement image  220  formed on the sheet P with light. The diffraction grating  202  is a spectral element that separates the light reflected from the measurement image  220  into respective wavelengths. The line sensor  203  includes n light receiving elements (n pixels). The calculation unit  204  performs various calculations based on the light intensity detected by each pixel of the line sensor  203 . The memory  205  stores various data. 
     The spectral sensor  200  detects the light intensity of the reflected light at intervals of 10 [nm] from 380 [nm] to 720 [nm], for example. In this case, n=34. That is, 34 pixels are arranged such that the first pixel receives light having a wavelength of 380 [nm] to 390 [nm], and the 34th pixel receives light having a wavelength of 710 [nm] to 720 [nm]. As illustrated in  FIG. 3 , the calculation unit  204  may include a reflectance calculation unit  240  that calculates the spectral reflectance based on the light intensity detected by each pixel, a Lab calculation unit  241  that calculates an L*a*b* value, and the like. The spectral sensor  200  may include a lens  206  that focuses light emitted from the white LED  201  onto the measurement image  220  on the sheet P or focuses light reflected from the measurement image  220  onto the diffraction grating  202 . 
     The spectral sensor  200  may include a white reference plate  250 . The spectral sensor  200  uses the white reference plate  250  to adjust the amount of light of the white LED  201 . The spectral sensor  200  causes the white LED  201  to emit light while the sheet P is not passing through the measurement position of the spectral sensor  200 , and receives, by the line sensor  203 , light reflected from the white reference plate  250 . The calculation unit  204  adjusts the emission intensity of the white LED  201  so that the light intensity of a predetermined pixel in the line sensor  203  becomes a predetermined value. The reflectance calculation unit  240  illustrated in  FIG. 3  may calculate the spectral reflectance Ri of the measurement image based on the following equation, for example. 
         Ri=Pi/Wi    (1)
 
     Here, Pi is a detection result of the line sensor  203  corresponding to the reflected light from the measurement image  220 . Wi is a detection result of the line sensor  203  corresponding to the reflected light from the white reference plate  250 . i is an index indicating a wavelength (i=1 to n). The spectral sensor  200  acquires the detection result Wi of the white reference plate  250  before the measurement image  220  arrives. The Lab calculation unit  241  calculates L*a*b* using the spectral reflectances R 1  to Rn of the measurement image. Since a calculation method for obtaining L*a*b* from spectral reflectance is known, a detailed description thereof will be omitted. 
     In  FIG. 3 , a CPU  300  (a determination unit  390 ) may determine a correction value X for correcting the measurement result of the spectral sensors  200   a  to  200   d  based on the measurement result of the spectral sensors  200   a  to  200   d  and the measurement result of the spectral sensor  200   e.  The RAM  309  is a storage device for storing the correction value X. The correction value X may be any of an offset value Of, a correction coefficient Co, and a conversion table T 1 , which will be described later. A correction unit  391   a  corrects L*a*b* which is a measurement result of the spectral sensors  200   a  to  200   d  to L*′a*′b*′ using the correction value X. This reduces individual differences between the spectral sensors  200   a  to  200   d.    
     Control System 
       FIG. 4  illustrates a control system of the image forming apparatus  100 . In this example, a digital front end (DFE)  500  is connected to the image forming apparatus  100 . The DFE  500  is an image processing device that executes raster image processing, color conversion, and the like. 
     The CPU  300  is a control circuit for controlling each unit of the image forming apparatus  100 . A ROM  304  is a storage device for storing control programs executed by the CPU  300  and required for executing various adjustments, processes, and the like. A RAM  309  is a system work memory for the CPU  300  to operate. An I/F unit  302  is an interface (communication circuit) connected to the DFE  500  and receives image data (e.g.: bitmap information with attributes) outputted from the DFE  500 . The attributes are information indicating types of image objects included in the image data inputted to the DFE  500 . Attributes include, for example, photographs, graphics (shapes), text (characters), etc. A gradation correction unit  316  performs gradation correction processing on the image data input from a reader  400  or the I/F unit  302 . That is, the gradation correction unit  316  functions as a correction unit that converts image data based on gradation correction conditions. The printer  101  functions as an image forming unit that forms an image on a sheet based on the image data corrected by the correction unit. Note that the gradation correction unit  316  individually performs gradation correction on the respective Y, M, C, and K image data. COPY may be added as an attribute to the image data inputted from the reader  400  to indicate copying. The gradation correction unit  316  performs gradation correction by referring to an LUT associated with an attribute stored in the memory  310 . LUT is an abbreviation of LookUp Table, and may be called a gradation correction condition or a gradation correction table. A halftone processing unit  317  also executes halftone processing (halftoning) according to an attribute. The reason why the halftone processing is changed according to the object is as follows. Characters printed on a sheet P have curves as well as straight lines. Therefore, unless the number of lines of the screen large, the outline of the character will not be reproduced smoothly. On the other hand, if halftoning is performed in relation to a photograph using a screen with many lines, there is a possibility that an image with a uniform density will not be reproducible. Therefore, the gradation correction unit  316  executes halftone processing suitable for the object, and converts the image data based on an LUT corresponding to the halftone processing. 
     The reason why the gradation correction is necessary is as follows. If the state of developer in the developing device  112  or the temperature or humidity inside the image forming apparatus  100  changes, a density characteristic (gradation characteristic) of the image formed by the image forming apparatus  100  will vary. The gradation correction unit  316  converts an input value (image signal value) of image data into a signal value for the printer  101  to form an image of a target density so that the density characteristic (gradation characteristic) of the image formed by the printer  101  becomes an ideal density characteristic. 
     The gradation correction unit  316  reads out from the memory  310  a gradation correction table (γLUT) corresponding to an attribute or a screen, and converts image data based on the γLUT. LUT_SC 1  is a gradation correction table corresponding to an image screen. LUT_SC 2  is a gradation correction table corresponding to a text screen. LUT_SC 3  is a gradation correction table corresponding to a COPY screen. The gradation correction table LUT_SC 4  is a gradation correction table corresponding to an error diffusion method. LUT_SC 1 , LUT_SC 2 , LUT_SC 3  and LUT_SC 4  correspond to the conversion conditions for converting image data. The γLUT generation unit  307  updates these γLUTs by executing calibration. 
     The gradation correction unit  316  may be realized by an integrated circuit such as an ASIC, or may be realized by a CPU  300  executing a program. ASIC is an abbreviation for Application Specific Integrated Circuit. The gradation correction unit  316  may convert the image data based on a gradation correction table, or may convert the image data based on a conversion formula. 
     The halftone processing unit  317  performs halftoning on image data converted by the gradation correction unit  316 , the halftoning being suitable for a type (attribute) of the image. The halftone processing unit  317 , based on an image screen, converts image data relating to an image and image data relating to graphics so that a photograph or a graphic becomes an image having excellent gradation property. The halftone processing unit  317 , based on a text screen, converts the image data relating to the text so that characters are clearly printed. When the operator selects the error diffusion method, the halftone processing unit  317  converts the image data based on the error diffusion method. Here, for example, when moire occurs in a high-resolution image, the operator selects the error diffusion method to suppress moire. The halftone processing unit  317  converts the image data of the original read by the reader  400  based on the COPY screen. 
     The image data to which screening was applied by the halftone processing unit  317  is output to the printer  101 . For example, the halftone processing unit  317  outputs yellow image data to the station  120 . The printer  101  forms an image on the sheet P based on the image data input from the halftone processing unit  317 . 
     A pattern generator  305  outputs image data of a measurement image used in calibration and correction value determination processing. The halftone processing unit  317  performs halftoning on the image data output from the pattern generator  305 . An image screen is applied to image data for updating LUT_SC 1 , which is a gradation correction table corresponding to an image screen. A text screen is applied to image data for updating LUT_SC 2 , which is a gradation correction table corresponding to a text screen. A COPY screen is applied to image data for updating LUT_SC 3 , which is a gradation correction table corresponding to a COPY screen. An error diffusion is applied to image data for updating LUT_SC 4 , which is a gradation correction table corresponding to error diffusion. The image data subjected to the halftoning is transferred to the printer  101 . The printer  101  forms an image for measurement on the sheet P based on the image data transferred from the halftone processing unit  317 . The CPU  300  conveys the sheet P on which the measurement image is formed toward the spectral sensor  200 , and causes the spectral sensor  200  to measure the measurement image on the sheet P. The spectral sensor  200  calculates the spectral reflectance of the measurement image  220  by the calculation unit  204 , and outputs it to a density conversion unit  306 . 
     The density conversion unit  306  converts the measurement results of the YMC measurement images into density values using a status A filter. The density conversion unit  306  converts the measurement results of a K (black) measurement image into density values using a visual filter. The status A filter and the visual filter are calculation methods defined by ISO-5/3. A printer controller  301  controls image forming conditions and generates a gradation correction table based on the measurement result (density value) converted by the density conversion unit  306 . The printer controller  301  includes, for example, an LPW adjustment unit  308  for adjusting the intensity of the laser of the exposure apparatus  103 , and a γLUT generation unit  307  for generating a gradation correction table. That is, the LPW adjustment unit  308  and the γLUT generation unit  307  are execution units that execute calibration. The LPW adjustment unit  308  determines the intensity of the laser so that the maximum value of the density of the measurement image becomes the target maximum density. The γLUT generation unit  307  generates a gradation correction table (γLUT) so that the gradation characteristic of the measurement image becomes an ideal gradation characteristic. The measurement image is formed for each color and for each screen. 
     As illustrated in  FIG. 4 , a correction unit  391   a  outputs the corrected L*′a*′b*′ to the density conversion unit  306 . In  FIG. 4 , the determination unit  390  and the correction unit  391   a  are separated from the CPU  300 , but the determination unit  390  and the correction unit  391   a  may be realized by the CPU  300 . As illustrated in  FIG. 5 , the correction unit  391   a  may be provided inside the calculation unit  204 . The calculation unit  204  may be realized by a CPU and a control program, or may be realized by hardware such as an ASIC. 
     The CPU  300  drives the motor M 1  to reciprocate the spectral sensor  200   e  in the main scanning direction. For example, the motor M 1  is connected to the spectral sensor  200   e  via a gear mechanism, a wire, or the like, and moves the spectral sensor  200   e.  Thus, the spectral sensor  200   e  is operable in the main scanning direction, in contrast to the fixed spectral sensors  200   a  to  200   d.    
     Arrangement of Spectral Sensors 
     As illustrated in  FIG. 6 , the spectral sensors  200   a  to  200   d  may be arranged along a direction orthogonal to the conveyance direction (main scanning direction). The measurement image  220  has a plurality of test patterns arranged corresponding to the spectral sensors  200   a  to  200   d.  When the sheet P is conveyed in the conveyance direction (sub-scanning direction), the spectral sensors  200   a  to  200   d  sequentially measure YMCKRGB test patterns. 
     The spectral sensor  200   e  measures the measurement image  220  by reciprocating in the main scanning direction. For example, by moving from left to right in  FIG. 6 , the spectral sensor  200   e  measures four test patterns of the Y color in order. Next, by moving from right to left in  FIG. 6 , the spectral sensor  200   e  measures four test patterns of the M color in order. The test patterns of the respective colors of the CKRGB are measured in the same manner. Note that the spectral sensor  200   e  may read four test patterns while always moving from left to right. 
     As illustrated in  FIG. 7 , the spectral sensors  200   a  and  200   b  and the spectral sensors  200   c  and  200   d  may be arranged at positions shifted in the conveyance direction. The arrangement of the YMCKRGB test patterns in the measurement image  220  is also changed in accordance with the arrangement of the spectral sensors  200   a  and  200   b  and the spectral sensors  200   c  and  200   d.  Such an arrangement is effective for small-sized paper having a narrow sheet width in the main scanning direction. 
     Incidentally, according to  FIG. 1 , the spectral sensor  200   e  is arranged on the downstream side of the spectral sensors  200   a  to  200   d  in the conveyance direction of the sheet P. However, the spectral sensor  200   e  may be arranged on the upstream side of the spectral sensors  200   a  to  200   d  in the conveyance direction of the sheet P. However, when the spectral sensor  200   e  reads the measurement image, it is necessary to stop the sheet P and read the test pattern of each color, and therefore it is convenient to arrange the spectral sensor  200   e  in the buffer  141 . 
     Flowchart 
       FIG. 8  is a main flowchart for describing calibration for correcting image forming conditions. The calibration includes a determination process for determining a correction value X. 
     In step  51 , the CPU  300  determines whether a correction value determination condition is satisfied. The determination condition is a condition for executing a process for determining the correction value. The condition may be, for example, that the user has instructed execution through the operation unit  180 , that the image forming apparatus  100  has been activated, or that an environmental condition variation process has exceeded a predetermined value. The environmental condition is a temperature, a humidity, or the like detected by an environmental sensor connected to the CPU  300 . In particular, the process of determining the correction value is performed prior to it becoming impossible to accurately correct the respective measured results of the spectral sensors  200   a  to  200   d  by the correction value X which is being held in the RAM  309 . When the determination condition is satisfied, the CPU  300  advances the process to step S 2 . When the determination condition is not satisfied, the CPU  300  advances the process to step S 3 . In step S 2 , the CPU  300  executes a process for determining the correction value. Details of the determination process will be described later with reference to  FIG. 9 . 
     In step S 3 , the CPU  300  determines whether a condition for starting calibration is satisfied. The start condition may be, for example, that the user has instructed execution through the operation unit  180 , that the image forming apparatus  100  has been activated, or that an environmental condition variation process has exceeded a predetermined value. The fact that the number of images to be formed exceeds a threshold may be adopted as the start condition. When the start condition is satisfied, the CPU  300  advances the process to step S 4 . If the start condition is not satisfied, the CPU  300  ends the calibration illustrated in  FIG. 8 . 
     In step S 4 , the CPU  300  executes calibration of image forming conditions. The calibration includes maximum density adjustment processing and gradation correction condition adjustment processing. The maximum density adjustment processing includes adjusting the charging potential, the intensity of the laser of the exposure apparatus  103  (exposure intensity), and the development bias. The adjustment process of the gradation correction condition includes a process of updating the γLUT. In both cases, the CPU  300  causes the pattern generator  305  to output the image data of the measurement image, and causes the printer  101  to form the measurement image on the sheet P. In addition, the CPU  300  causes the spectral sensors  200   a  to  200   d  to measure the measurement images, adjusts the charging potential, the exposure intensity, and the development biases based on the measurement results, and corrects the gradation correction condition. In any case, the CPU  300  corrects the measurement results of the spectral sensors  200   a  to  200   d  using the correction value X determined in step S 2 , and modifies the image forming conditions using the corrected measurement results. This also improves the accuracy of the calibration. 
     Details of Correction Value Determination Process 
       FIG. 9  is a flowchart for describing a process for determining a correction value. In step S 11 , the CPU  300  (determination unit  390 ) uses the pattern generator  305  and the printer  101  to form a measurement image including test patterns for the determination process on the sheet P. The pattern generator  305  outputs image data designated by the determination unit  390 . For example, YMCKRGB test patterns illustrated in  FIG. 6  and  FIG. 7  are produced at 100% density. In step S 12 , the CPU  300  (determination unit  390 ) controls the conveyance rollers and the flapper  132  to convey the sheet P to the spectral sensors  200   a  to  200   d.    
     In step S 13 , the CPU  300  (determination unit  390 ) measures the measurement image formed on the sheet P using the spectral sensors  200   a  to  200   d.  Here, a measurement result (L*a*b*) is acquired for each of the spectral sensors  200   a  to  200   d.  The measurement result of the Y color of the spectral sensor  200   a  may be referred to as L*a*b*-Ya. Similarly, the measurement result of the M color of the spectral sensor  200   b  may be referred to as L*a*b*-Mb. In this manner, a combination of lowercase alphabet for distinguishing the spectral sensors  200   a  to  200   d  and uppercase alphabet for indicating color may be used to identify the measurement results. 
     In step S 14 , the CPU  300  (determination unit  390 ) controls the conveyance rollers and the flappers  133  and  134  to convey the sheet P to the spectral sensor  200   e.  In step S 15 , the CPU  300  (determination unit  390 ) measures the measurement image formed on the sheet P using the spectral sensor  200   e.  The determination unit  390  drives the motor M 1  to cause the spectral sensor  200   e  to measure the YMCKRGB test patterns while reciprocating the spectral sensor  200   e.  The determination unit  390  stops the conveyance roller upon reading of the test pattern of each color. This is because the reciprocating motion of the spectral sensor  200   e  requires a considerable amount of time. When the spectral sensors  200   a  to  200   d  measure the measurement images, the conveyance roller does not have to be stopped. This is because the spectral sensors  200   a  to  200   d  are fixed and do not reciprocate. Here, the measurement results (L*a*b*-Yae, L*a*b*-Ybe, . . . , L*a*b*-Bde) of the spectral sensor  200   e  are obtained. Here, L*a*b*-Yae represents the measurement result for the Y color measured by the spectral sensor  200   e  corresponding to the measurement result L*a*b*-Ya for the Y color measured by the spectral sensor  200   a.  In other words, L*a*b*-Ya and L*a*b*-Yae indicate the measurement results for the leftmost test pattern of the four Y color test patterns illustrated in  FIG. 6 . Similarly, L*a*b*-Ybe represents the measurement result for the Y color measured by the spectral sensor  200   e  corresponding to the measurement result L*a*b*-Yb for the Y color measured by the spectral sensor  200   b.  In other words, L*a*b*-Yb and L*a*b*-Ybe indicate the measurement results for the second leftmost test pattern of the four Y color test patterns illustrated in  FIG. 6 . Since all of L*a*b*-Ya to L*a*b*-Ba are the results of the spectral sensor  200   a,  they may be collectively referred to as L*a*b*-a. In this manner, the spectral sensors  200   a  to  200   d  and the spectral sensor  200   e  measure test patterns respectively formed at the same positions. 
     In step S 16 , a CPU  300  (a determination unit  390 ) may determine correction values Xa, Xb, Xc, and Xd for correcting the measurement results of the spectral sensors  200   a  to  200   d  using the measurement results of the spectral sensors  200   a  to  200   d  and the measurement results of the spectral sensor  200   e.  The correction values Xa, Xb, Xc, and Xd can be determined for each of L*, a*, and b*. 
       FIG. 10A  illustrates the measurement result L*a*b*-a of the spectral sensor  200   a  and the measurement result L*a*b*-e of the spectral sensor  200   e  in the a*-b* plane. The a*-b* plane is used for simplicity of explanation. As illustrated in  FIGS. 10A and 10B , it can be seen that there are individual differences between the spectral sensor  200   a  and the spectral sensor  200   e.  Therefore, the determination unit  390  determines the offset value Ofa for matching the measurement result L*a*b*-a of the spectral sensor  200   a  with the measurement result L*a*b*-e of the spectral sensor  200   e.  Although not illustrated here, similar individual differences exist in the spectral sensors  200   b  to  200   d.  Therefore, the determination unit  390  determines offset values Ofb, Ofc, and Ofd for matching the measurement results L*a*b*-b, L*a*b*-c, and L*a*b*-d of the spectral sensors  200   b  to  200   d  with the measurement result L*a*b*-e. The offset value is obtained for each of L*, a*, and b*. The determination unit  390  writes the offset value Of into the RAM  309 . 
     Correction of the measurement result with the offset value Of thus obtained improves the measurement accuracy of L*a*b*. For example, when the test pattern of Y [100%] was tested, ΔE when the measurement results of the spectral sensors  200   a  to  200   d  were not corrected was 2.2. On the other hand, by correcting the measurement results, ΔE became 1.2, and a significant improvement was observed. 
     In the first embodiment, the configuration of the spectral sensor  200   e  is the same as the configuration of the spectral sensors  200   a  to  200   d.  If a sensor having higher performance than the spectral sensors  200   a  to  200   d  is employed as the spectral sensor  200   e,  the correction accuracy will be further improved. 
     Second Embodiment 
     As illustrated in  FIG. 2 , the spectral sensors  200   a  to  200   e  have a white LED  201 . Since there are individual differences in the white LED  201 , these individual differences may lead to errors in the measured results. The light emission amount of the white LED  201  of the spectral sensors  200   a  to  200   e  is adjusted to a predetermined light emission amount by using a result of measuring the white reference plate  250  by the line sensor  203 . However, there are also individual differences in the white reference plate  250 . 
       FIG. 10B  illustrates differences in the measurement results caused by differences in the light emission amount. In this example, it is understood that the light emission amount of the spectral sensor  200   a  is smaller than the light emission amount of the spectral sensor  200   e.  That is, in the method of the first embodiment, the measurement results are offset in the a*-b* plane, but the measurement results of the spectral sensors  200   a  to  200   d  do not coincide with the spectral sensor  200   e  by that alone. That is, a multiplication-type correction coefficient for correcting the difference in the light emission amount may be necessary. 
     Therefore, the measurement image  220  may include test patterns for correcting a difference in the light emission amount. The CPU  300  executes steps S 11  to S 16 . That is, the determination unit  390  causes the spectral sensors  200   a  to  200   e  to measure the test patterns for correcting the difference in the light emission amount, and determines the correction value X (a correction coefficient Co) for reducing the error of the measurement result L*a*b based on the difference in the light emission amount. This test patterns are test patterns of a size that is commonly read by the spectral sensors  200   a  to  200   e.  The determination unit  390  determines the correction coefficient Co so that the measurement results L*a*b* of the spectral sensors  200   a  to  200   e  coincide with each other, and stores the correction coefficient Co in the RAM  309 . For example, the determination unit  390  may determine the correction coefficient Co such that the measurement result L*a*b* of the spectral sensor  200   e  matches the measurement results L*a*b* of the spectral sensors  200   a  to  200   e,  and may store the correction coefficient Co in the RAM  309 . As described above, the spectral sensor  200   e  may be employed as a reference sensor, but any one of the spectral sensors  200   a  to  200   d  may be employed as the reference sensor. The correction coefficient Co is a multiplication coefficient. It has been found that ΔE for the spectral sensors  200   a  to  200   d  is reduced to 1.0 by employing the correction coefficient Co in addition to the correction value X. 
     Third Embodiment 
     In the first embodiment, an offset value Of which is added to or subtracted from the measurement result is proposed. In the second embodiment, a correction coefficient Co which is multiplied by the measurement result is further proposed. Since these are correction values basically determined by the test pattern of  100 % density, there is a possibility that a correction residual is generated for other densities. In the third embodiment, a conversion table T 1  for converting an actual measurement result into a corrected measurement result is proposed as the correction value X. 
     The CPU  300  executes steps S 11  to S 16 . In particular, the determination unit  390  forms the measurement image  220  including a large number of test patterns (e.g.:  1028  test patterns) on the sheet P in step S 11 . For example, as  FIG. 11  illustrates, a number of test patterns are generated to correspond to various coordinates in the a*-b* plane. In steps S 12  to S 15 , test patterns are measured by the spectral sensors  200   a  to  200   e.    
     In step S 16 , the determination unit  390  determines one correction coefficient for each test pattern. For example, it is assumed that the first test pattern was a pattern formed by mixing colors of Y:10%, M:10%, and C:10%. The spectral sensor  200   a  and the spectral sensor  200   e  each measure a first test pattern. The determination unit  390  obtains a difference between the measurement result of the spectral sensor  200   a  and the measurement result of the spectral sensor  200   e  as a correction coefficient. This correction coefficient is determined for each of L*, a*, and b*. For example, the correction coefficient of L* is calculated as +0.01, the correction coefficient of a* is calculated as +0.02, and the correction coefficient of b* is calculated as −0.01. The determination unit  390  performs this operation on a plurality of test patterns having different YMCK density combinations. Finally, the conversion table T 1  for converting the measurement result L*b*a* into the measurement result L*′b*′a*′ for each of the spectral sensors  200   a  to  200   d  is completed and stored in the RAM  309 . 
     In the first embodiment, generally test patterns having a density of 100% are used, but in the present embodiment, since test patterns having various densities are used, a conversion table T 1  capable of correcting measurement results with high accuracy at various densities is created. The correction unit  391   a  converts the actual measurement result L*b*a* into the measurement result L*′b*′a*′ using the conversion table T 1 . This improved the ΔE for the spectral sensors  200   a  to  200   d  to 0.8. 
     Fourth Embodiment 
     In the first to third embodiments, the measurement result L*a*b* is directly corrected by the correction value X. However, any parameter from the output value of the line sensor  203  to the measurement result L*a*b* may be corrected. Therefore, as an example, a method of correcting the measurement result L*a*b* by correcting the spectral reflectance Ri is proposed. 
       FIG. 12  is a diagram illustrating spectral characteristics of nine spectral sensors. The horizontal axis represents wavelength. The vertical axis represents the spectral reflectance. Especially, in spectral sensors employing an inexpensive light emitting element, individual differences in spectral reflectance become large. As illustrated in  FIG. 12 , since the spectral reflectance differs for each wavelength, a correction value X for the spectral reflectance for each wavelength is necessary. However, the work to determine the correction value X over the entire range of wavelengths takes a long time, and the storage capacity of the RAM  309  must be increased. Therefore, the determination unit  390  creates a correction table T 2  for correcting the actual spectral reflectance Ri to the corrected spectral reflectance Ri′ for a wavelength range in which the spectral reflectance varies widely. In the case illustrated in  FIG. 12 , a wavelength range of at least 500 nm to 550 nm may be sufficient, but here, a correction table T 2  may be created for every 10 nm in the range of 400 nm to 700 nm. 
     The CPU  300  executes steps S 11  to S 16 . In steps S 11  to S 15 , the determination unit  390  causes the spectral sensors  200   a  to  200   d  and the spectral sensor  200   e  to measure the measurement image  220  as described above. Here, the spectral reflectance Ri is obtained as a measurement result. In step S 16 , the determination unit  390  determines the correction value of the spectral reflectance so that the spectral reflectance Ri of each of the spectral sensors  200   a  to  200   d  matches the spectral reflectance Ri of the spectral sensor  200   e.  A collection of correction values obtained for each wavelength is a correction table T 2 . The determination unit  390  stores the correction table T 2  as the correction value X in the memory  205 . 
     As illustrated in  FIG. 13 , a correction unit  391   b  references the correction table T 2  held in the memory  205  and acquires a correction value Xi for each pixel (each wavelength) in the line sensor  203 . Further, the correction unit  391   b  multiplies the spectral reflectance Ri output from the reflectance calculation unit  240  by the correction value Xi to obtain the corrected spectral reflectance Ri′, and outputs the obtained spectral reflectance Ri′ to the Lab calculation unit  241 . As a result, the measurement result output from the Lab calculation unit  241  becomes L*′a*′b*′. Note that it has been found that ΔE for the spectral sensors  200   a  to  200   d  is reduced to  0 . 4  by applying the fourth embodiment. When the correction unit  391   b  is provided, the correction unit  391   a  may be omitted. Both the correction unit  391   a  and the correction unit  391   b  may be provided. 
     Summary 
     As illustrated in  FIG. 1 , the conveyance paths  135  and  139  function as a conveyance unit that conveys the sheet P in a first direction. The stations  120  to  123  function as an image forming unit for forming an image on the sheet P. The spectral sensors  200   a  to  200   d  function as a plurality of first spectral sensors for measuring a first measurement image formed on the sheet P by the image forming unit. As illustrated in  FIG. 6  and the like, the first measurement image (e.g.: a yellow test pattern) is formed along a second direction (e.g.: a main scanning direction) intersecting the first direction. The spectral sensor  200   e  functions as a second spectral sensor for measuring the first measurement image formed on the sheet P. The motor M 1  functions as a movement unit that moves the second spectral sensor along a third direction intersecting the first direction. The third direction may be a direction parallel to the main scanning direction. When the conveying speed of the sheet P is low, the third direction may be inclined with respect to the main scanning direction. Basically, the third direction and the conveyance direction of the sheet P are orthogonal to each other. The determination unit  390  functions as a determination unit that determines a correction value for correcting an output value of each of the plurality of first spectral sensors. The determination unit  390  determines the correction value based on a measurement result of the first measurement image acquired by the plurality of first spectral sensors and a measurement result of the first measurement image acquired by the second spectral sensor while the second spectral sensor is being moved in the third direction by the movement unit. The correction units  391   a  and  391   b  correct an output value output from each of the plurality of first spectral sensors with the correction value determined by the determination unit by measuring a second measurement image that is formed by the image forming unit and that is for modifying an image forming condition of the image forming unit. The correction units  391   a  and  391   b  may be collectively referred to as the correction unit  391 . The second measurement image for modifying the image forming condition is a measurement image for calibration, and may be fundamentally different from the measurement image  220  for correcting the measurement result. The LUT generation unit  307  and the LPW adjustment unit  308  function as a modification unit that modifies the image forming condition based on the output value corrected by the correction unit. As described above, according to the present embodiment, individual differences between a plurality of spectral sensors are accurately corrected. 
     The plurality of first spectral sensors may all be spectral sensors of the same specification. The white LED  201  is an exemplary light emitting element that outputs light onto the sheet P. The line sensor  203  is an example of a light receiving element that receives reflected light from the sheet P or an image formed on the sheet P. The reflectance calculation unit  240  is an example of a first calculation unit that calculates the spectral reflectance based on the light reception result of the light receiving element. The Lab calculation unit  241  is an example of a second calculation unit that calculates chromaticity, which is an output value, based on the spectral reflectance. The correction unit  391  may correct the output value by correcting the spectral reflectance or chromaticity using the correction value. 
     Each of the plurality of first spectral sensors may include a light emitting element, a light receiving element, a first calculation unit, a second calculation unit, and the like. Further, the second spectral sensor may have a light emitting element, a light receiving element, and the like similarly to the first spectral sensor. That is, the first spectral sensor and the second spectral sensor may be of the same model (the same product or the same specification). The first spectral sensor and the second spectral sensor may be different products (of different specifications). For example, the measurement accuracy of the second spectral sensor may be higher than the measurement accuracy of the first spectral sensor. In this case, the correction accuracy will be further improved. 
     As described in the first embodiment, the correction value may be an offset value Of to be added to the chromaticity. The correction value may be a coefficient to be multiplied with the chromaticity (e.g.: the correction coefficient Co). The output value may be L*a*b* data in the L*a*b* color space. The determination unit  390  may create a conversion table (e.g.: the correction table T 2  or the conversion table T 1 ) for converting the output value into the output value corrected by the correction value. The correction unit  391  may convert the output value into a corrected output value using a conversion table. 
     As illustrated in  FIG. 2 , the light receiving element may have n pixels arranged or configured to receive light of different wavelengths. The correction unit  391  may correct the output values of m pixels (n&gt;=m) that receive light of a predetermined range of wavelengths among the n pixels. For example, the n pixels may be arranged to receive light at wavelengths ranging from 380 nanometers to 720 nanometers. The m pixels may be arranged to receive light at wavelengths ranging from 400 nanometers to 700 nanometers. As described with reference to  FIG. 12 , the m pixels may be determined so as to correspond to a wavelength range having a large variation in spectral reflectance in the plurality of spectral sensors  200   a  to  200   d.  For example, the m pixels may be arranged to receive light at wavelengths ranging from 500 nanometers to 550 nanometers. 
     As illustrated in  FIG. 7 , at least two spectral sensors of the plurality of first spectral sensors may be arranged along the second direction. This reduces the number of times the second spectral sensor reciprocates along the second direction. As illustrated in  FIGS. 6 and 7 , the second direction may be orthogonal to the first direction. However, the angle at which the second direction and the first direction intersect may be slightly deviated from 90°. As illustrated in  FIGS. 6 and 7 , the third direction (moving direction of the spectral sensor  200   e ) may be parallel to the second direction (main scanning direction). The motor Ml may reciprocate the second spectral sensor along the third direction. The second spectral sensor may measure the first measurement image in each of a forward path and a return path in the reciprocating motion. This makes it possible to efficiently read the test pattern constituting the measurement image  220 . 
     Other Embodiments 
     Embodiment(s) of the present invention can also be realized by a computer of a system or apparatus that reads out and executes computer executable instructions (e.g., one or more programs) recorded on a storage medium (which may also be referred to more fully as ‘non-transitory computer-readable storage medium’) to perform the functions of one or more of the above-described embodiment(s) and/or that includes one or more circuits (e.g., application specific integrated circuit (ASIC)) for performing the functions of one or more of the above-described embodiment(s), and by a method performed by the computer of the system or apparatus by, for example, reading out and executing the computer executable instructions from the storage medium to perform the functions of one or more of the above-described embodiment(s) and/or controlling the one or more circuits to perform the functions of one or more of the above-described embodiment(s). The computer may comprise one or more processors (e.g., central processing unit (CPU), micro processing unit (MPU)) and may include a network of separate computers or separate processors to read out and execute the computer executable instructions. The computer executable instructions may be provided to the computer, for example, from a network or the storage medium. The storage medium may include, for example, one or more of a hard disk, a random-access memory (RAM), a read only memory (ROM), a storage of distributed computing systems, an optical disk (such as a compact disc (CD), digital versatile disc (DVD), or Blu-ray Disc (BD)™), a flash memory device, a memory card, and the like. 
     While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures and functions. 
     This application claims the benefit of Japanese Patent Application No. 2019-048744, filed Mar. 15, 2019 which is hereby incorporated by reference herein in its entirety.