Patent Publication Number: US-11048187-B1

Title: Exposure control device, image forming apparatus, and non-transitory computer readable medium

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is based on and claims priority under 35 USC 119 from Japanese Patent Application No. 2020-045015 filed Mar. 16, 2020. 
     BACKGROUND 
     1. Technical Field 
     The present disclosure relates to an exposure control device, an image forming apparatus, and a non-transitory computer readable medium. 
     2. Related Art 
     When an image is formed, density nonuniformity may occur due to, for example, eccentricity of a developing roller or a difference in a developing ability between a center and an end portion of the developing roller in an axial direction. It has been studied how to correct such density nonuniformity so as to form a good image without the density nonuniformity. 
     Japanese Patent No. 5825862 discloses that density nonuniformity is prevented by calculating correction pixel values according to pixel values and forming an image using the calculated correction pixel values (corrected image data). 
     SUMMARY 
     The pixel value is represented by a digital value within a certain range such as 0 to 255. Therefore, when the pixel value is close to 0, that is, a density is low, even if the pixel value is different by 1, the density is greatly different, and there is a risk of overcorrection. When the pixel value is close to 255, that is, the density is high, since the pixel value cannot be corrected to 255 or more, the correction may be insufficient. 
     Aspects of non-limiting embodiments of the present disclosure relate to an exposure control device, an image forming apparatus, and a non-transitory computer readable medium that improve accuracy of correction as compared with a case of correcting pixel values. 
     Aspects of certain non-limiting embodiments of the present disclosure address the above advantages and/or other advantages not described above. However, aspects of the non-limiting embodiments are not required to address the advantages described above, and aspects of the non-limiting embodiments of the present disclosure may not address advantages described above. 
     According to an aspect of the present disclosure, there is provided an exposure control device includes an exposure light amount calculator and an exposure controller. The exposure light amount calculator is configured to obtain, for each of plural correction points that are associated with a respective one of primary correction values and are separated from each other, a correction factor for correcting the primary correction value of the correction point, based on a pixel value of the correction point, calculate, for each correction point, a secondary correction value based on the primary correction value and the correction factor of the correction point, and calculate a distribution of the secondary correction values on an image based on the plural secondary correction values of the plural correction points. The exposure controller is configured to cause an exposure unit to form a latent image by exposure to light having a corrected light amount obtained by correcting a light amount corresponding to a pixel value of each point based on the secondary correction value of the point. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Exemplary embodiment(s) of the present disclosure will be described in detail based on the following figures, wherein: 
         FIG. 1  is a schematic configuration diagram illustrating an image forming apparatus according to an exemplary embodiment of the present disclosure; 
         FIG. 2  is a schematic diagram illustrating a configuration around an image forming unit; 
         FIG. 3  is a block diagram illustrating a configuration of an exposure control device according to a first exemplary embodiment of the present disclosure; 
         FIG. 4  is a diagram illustrating a flowchart of a procedure of creating a primary correction value table; 
         FIG. 5  is a diagram illustrating correction points; 
         FIG. 6  is a diagram illustrating an example of the primary correction value table; 
         FIG. 7  is a diagram illustrating an example of a correction magnification lookup table (LUT); 
         FIG. 8  is a diagram illustrating a flowchart of a process executed on a light amount controller of the exposure control device illustrated in  FIG. 3  when a user image is formed; 
         FIG. 9  is a diagram illustrating an image of a region that is determined according to a screen; 
         FIG. 10  is a diagram illustrating estimation errors of Cin relating to types of the screen and widths of a region in a process direction; and 
         FIG. 11  is a block diagram illustrating a configuration of an exposure control device according to a second exemplary embodiment of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Hereinafter, exemplary embodiments of the present disclosure will be described. 
       FIG. 1  is a schematic configuration diagram illustrating an image forming apparatus  10  according to an exemplary embodiment of the present disclosure. The image forming apparatus  10  includes an exposure control device and an exposure control program according to the exemplary embodiment of the present disclosure. 
     The image forming apparatus  10  receives image data from a personal computer (which is not illustrated, and is hereinafter abbreviated as a “PC”) and forms an image on a sheet based on the image data. 
     The image forming apparatus  10  includes two housings of a first housing  10   a  and a second housing  10   b  that are connected to each other. Respective members that constitute the image forming apparatus  10  are separately provided in the two housings  10   a  and  10   b.    
     The image forming apparatus  10  is configured to form an image using toners of four colors. Four toner cartridges  11 Y,  11 M,  11 C, and  11 K that accommodate the toners of the respective colors are arranged in an upper portion of the first housing  10   a.    
     Herein, alphabets in reference numerals represent the colors of the toners accommodated in the toner cartridges. Among the alphabets, Y represents yellow, M represents magenta, C represents cyan, and K represents black. 
     Hereinafter, when it is not necessary to distinguish the colors, the alphabets indicating the colors may be omitted, and the reference numeral “ 11 ” is simply assigned to the toner cartridges. When it is necessary to distinguish the colors, the reference numerals each followed by a respective one of the above-described alphabets representing the colors will be used. The same applies to elements other than the toner cartridges  11 . 
     The toner in each toner cartridge  11  is supplied to a developing unit  133  that constitutes an image forming unit  13  (which will be described later). Each toner cartridge  11  is replaceable. When the toner cartridge  11  becomes empty, the toner cartridge  11  is replaced with a new toner cartridge  11  accommodating the toner of the same color. 
     In the first housing  10   a , four exposure units  12  and four image forming units  13  are provided below the toner cartridges  11 . 
       FIG. 2  is a schematic diagram illustrating a configuration around one image forming unit  13 . 
     The image forming unit  13  includes a drum-shaped image carrier  131  that rotates in a direction of an arrow A. A charging unit  132 , the developing unit  133 , a cleaning blade  134 , and a static eliminator  135  are disposed around the image carrier  131 . The exposure unit  12  is disposed above the image carrier  131 . A primary transfer roller  15  is disposed at a position where an intermediate transfer belt  14  (which will be described later) is sandwiched between the image carrier  131  and the primary transfer roller  15 . 
     The image carrier  131  is charged by the charging unit  132  while rotating in the direction of the arrow A. 
     The exposure unit  12  repeatedly scans the image carrier  131  with an exposure beam L (which is modulated according to the image data) in a direction perpendicular to a paper surface of  FIG. 2 . The exposure unit  12  forms an electrostatic latent image on the image carrier  131  by repeatedly scanning with the exposure beam L. 
     A developer containing the toner and a carrier is accommodated in the developing unit  133 . The developing unit  133  includes a developing roller  133   a . The developing roller  133   a  carries the developer accommodated in the developing unit  133  to a position where the developing roller  133   a  faces the image carrier  131 , while rotating in a direction of an arrow R. The developing roller  133   a  develops the electrostatic latent image on the image carrier  131  with the toner in the developer to form a toner image on the image carrier  131 . The toner is supplied from the corresponding toner cartridge  11  (see  FIG. 1 ) such that a predetermined amount of the toner is accommodated in the developing unit  133 . 
     The toner image formed on the image carrier  131  by an action of the developing unit  133  is transferred onto the intermediate transfer belt  14  that moves in a direction of an arrow B by an action of the primary transfer roller  15  that rotates in a direction of an arrow C while receiving application of a transfer bias. 
     The toner remaining on the image carrier  131  after the transfer is scraped and collected from the image carrier  131  by the cleaning blade  134 . Then, the image carrier  131  is neutralized by the static eliminator  135  to erase the latent image remaining therein, and is newly charged by the charging unit  132 . 
     Returning to  FIG. 1 , the description will be continued. 
     Below the four image forming units  13 , the endless intermediate transfer belt  14  is provided. The intermediate transfer belt  14  is supported by plural rollers  16  including a driving roller  16   a  and a backup roller  16   b . The intermediate transfer belt  14  circularly moves in the direction of the arrow B while being in contact with the image carriers  131  that constitute the image forming unit  13 . 
     A secondary transfer roller  17  is provided at a position where the secondary transfer roller  17  faces the backup roller  16   b  with the intermediate transfer belt  14  sandwiched therebetween. The toner images sequentially transferred to the intermediate transfer belt  14  in a superimposed manner by the action of the primary transfer rollers  15  provided corresponding to the respective image forming units  13  are further transported by the intermediate transfer belt  14  in the direction of the arrow B. Then, the toner images on the intermediate transfer belt  14  are secondarily transferred by an action of the secondary transfer roller  17  onto a sheet transported to a position sandwiched between the intermediate transfer belt  14  and the secondary transfer roller  17 . Accordingly, an unfixed toner image is formed on the sheet. 
     Two sheet accommodating units  18   a  and  18   b  are provided in a lower portion of the first housing  10   a . A large number of sheets P are accommodated in each sheet accommodating units  18   a  and  18   b  in a stacked state. The paper P is taken out from the sheet accommodating units  18   a  and  18   b  during image formation. Bottom plates  181   a  and  181   b  rise as the number of sheets P accommodated in the sheet accommodating units  18   a  and  18   b  decreases. 
     When the image is formed, the uppermost sheet among the sheets P accommodated in one of the sheet accommodating units  18   a  and  18   b , which is designated automatically or manually by an operator, is taken out by a pickup roller  19   a . When the plural sheets P are taken out at once, a retard roller  19   b  reliably separates one sheet from the plural sheets P. Then, the one sheet is transported by a transport roller  19  onto transport paths  20   a ,  20   b , and  20   c , and a leading end of the transported sheet reaches a registration roller  19   c . The first housing  10   a  is provided with an intake port  111  through which the sheet is taken in from the outside of the first housing  10   a . When the paper is taken in from the intake port  111 , the taken-in sheet is transported on the transport paths  20   d  and  20   c , and a leading end of the sheet reaches the registration roller  19   c . The registration roller  19   c  corrects a posture of the transported sheet, adjusts subsequent timing at which the sheet is fed, and further feeds the sheet downstream in a transport direction. 
     The registration roller  19   c  feeds the sheet such that the sheet is transported to a position of the secondary transfer roller  17  at the same timing as the toner image on the intermediate transfer belt  14  is transported to the position of the secondary transfer roller  17 . 
     The sheet on which the toner image is transferred by the action of the secondary transfer roller  17  is transported by a transport belt  21 , enters the second housing  10   b , and reaches a fixing unit  22 . The fixing unit  22  includes a heating belt  221  and a pressure roller  222 . The sheet transported to the fixing unit  22  is heated and pressed while being sandwiched between the heating belt  221  and the pressure roller  222 , so that the toner image on the sheet is fixed on the sheet. The sheet that has passed through the fixing unit  22  is transported by a transport belt  23 , and reaches a decurler  24 . A warp of the sheet is corrected by the decurler  24 . 
     The sheet that has passed through the decurler  24  is cooled by a cooling unit  25 . The cooling unit  25  cools the sheet by sandwiching the sheet between two endless belts  251  and  252 . An optical measuring unit  26  measures an image (that is, the fixed toner image) on the sheet discharged from the cooling unit  25 . The optical measuring unit  26  monitors whether the image is correctly formed on the sheet during normal image formation. During adjustment, the optical measuring unit  26  performs measurement for the adjustment, for example, in the following manners. That is, (i) the image forming apparatus  10  arranges various charts and color patches on a sheet, and the optical measuring unit  26  measures the charts and color patches for color tone adjustment, or (ii) the image forming apparatus  10  forms an image for adjustment of an image formation position or image magnification on a sheet, and the optical measuring unit  26  measures this image to adjust the image formation position or the image magnification. Furthermore, the image forming apparatus  10  forms an image having a uniform color and a uniform density on a sheet, and the optical measuring unit  26  measures the image to check if scratch or density unevenness is generated on the image. 
     The sheet that has passed through the optical measuring unit  26  is discharged onto a sheet discharge table  28  by a discharge roller  27 . 
     After the toner image is secondarily transferred onto the sheet by the action of the secondary transfer roller  17 , the intermediate transfer belt  14  still moves in the direction of the arrow B and reaches a cleaner  41 . The cleaner  41  removes the toner remaining on the intermediate transfer belt  14  from the intermediate transfer belt  14 . 
     A process of forming an image only on a first surface of the sheet has been described above. A process of forming images on both surfaces of the sheet will be described below. In this case, the image is formed on the first surface of the sheet by the same process as above, and then the sheet passes through the optical measuring unit  26 . The sheet that has passed through the optical measuring unit  26  enters a transport path  20   e  before reaching the discharge roller  27 , is transported on the transport path  20   e  and further enters a transport path  20   f . When the sheet enters the transport path  20   f , rotation directions of transport rollers that constitute the transport path  20   f  reverse, and the sheet is fed out in an opposite direction from the transport path  20   f , returns to the first housing  10   a , is transported on the transport paths  20   b  and  20   c , and reaches the registration roller  19   c . At this time, the sheet is in a posture in which a second surface on which the image has not yet been formed faces the intermediate transfer belt  14 . By the time the sheet reaches the registration roller  19   c  through such a transport path, the image forming unit  13  forms toner images corresponding to an image to be formed on the second surface of the sheet and transfers the toner images onto the intermediate transfer belt  14 . Thereafter, similar to the manner in which the image is formed on the first surface of the sheet, the sheet is fed out from the registration roller  19   c , and the toner images are transferred to the second surface of the sheet by the action of the secondary transfer roller  17 , and then the sheet passes through the fixing unit  22 , the decurler  24 , the cooling unit  25 , and the optical measuring unit  26 , and is then discharged onto the sheet discharge table  28  by the discharge roller  27 . 
     An image processor and controller  30  is provided in an upper part of the second housing  10   b  of the image forming apparatus  10 . The image processor and controller  30  includes a memory, an operating circuit, and a control circuit. The memory stores the image data and the like sent from the outside. The operating circuit performs various processing, such as image processing, for the image data. The control circuit controls the overall image forming apparatus  10 . The image processor and controller  30  has an operating function of executing a program. The operating circuit and the control circuit that constitute the image processor and controller  30  provide functions implemented by a combination of hardware of the image processor and controller  30  and the program executed by the image processor and controller  30 . 
     A power supply unit  33  is provided below the image processor and controller  30 . The power supply unit  33  supplies necessary power to each member of the image forming apparatus  10 . 
     The image forming apparatus  10  includes an environment sensor  34  that measures environmental temperature and humidity inside the image forming apparatus  10 . The temperature and humidity measured by the environment sensor  34  are reported to the image processor and controller  30  and are reflected in various control of the image forming apparatus  10 . 
     A monitor  31  and an operation panel  32  are placed on a lower step of the second housing  10   b . The monitor  31  displays various statuses of the image forming apparatus  10 . The operation panel  32  is operated by an operator. 
     The overall image forming apparatus has been described above. Hereinafter, description will be made on exposure control that is a feature of the present exemplary embodiment, that is, light amount control of the exposure beam L emitted from the exposure unit  12 . 
       FIG. 3  is a block diagram illustrating a configuration of an exposure control device  50 A according to a first exemplary embodiment of the present disclosure. 
       FIG. 1  illustrates the image forming apparatus  10  that forms a color image using the toners of the four colors of Y, M, C, and K. Description which will be made with reference to  FIG. 3  and subsequent drawings is common to those four colors. Thus, one color will be illustrated and described below. 
     Except for a light amount adjuster  53 , the exposure control device  50 A is established in the image processor and controller  30  illustrated in  FIG. 1  by the image processor and controller  30  executing the exposure control program. The light amount adjuster  53  is provided in the exposure unit  12 . 
     The exposure control device  50 A includes an image editing unit  51 , a data converter  52 , the light amount adjuster  53 , and a light amount controller  54 . Herein, the light amount controller  54  includes a primary correction value table  61  and a correction magnification lookup table (LUT)  62 . 
     The image data transmitted from the external PC is input to the image editing unit  51 . The image data includes (i) information indicating components on data that constitutes an image, such as graphic data and character data, and (ii) information indicating a type of a screen for halftone dot printing. The image editing unit  51  generates multi-level data of each of pixels constituting the image by integrating the input data in various formats. The multi-level data of each pixel has a numerical value of in a range of 0 to 255. In a screen image (halftone dot image), a pixel value of 0 refers to a dot percent of 0%, and a pixel value of 255 refers to a dot percent of 100%. Other numerical values are also similar. 
     The multi-level data generated in the image editing unit  51  is input to the data converter  52 . Information on the screen is also passed to the data converter  52 . The data converter  52  converts the multi-level data received from the image editing unit  51  into binary data representing a screen image (halftone dot image) according to an instructed screen. Two values of the binary data will be described as white and black for the sake of understanding. It is noted that this notation is used on data, but an actual color is not white or black. The actual color is different for each of the toners of the four colors. 
     The binary data is data representing a pixel of multi-level data using a screen image (halftone dot image) having a set of white and black dots. For example, when a certain pixel has a dot percent of 50% that is a central value of 127 in the multi-level data from 0 to 255, the pixel is represented by half white dots and half black dots that are arranged according to a designated screen. The same applies to the multi-level data of other values. Herein, the white dots on the image refer to dots that are not irradiated with the exposure beam L, and the black dots refer to dots that are irradiated with the exposure beam L. 
     The binary data generated in the data converter  52  is input to the light amount adjuster  53 . The binary data is also input to the light amount controller  54 . Description on the light amount controller  54  will be given later. 
     The light amount adjuster  53  is provided in the exposure unit  12  illustrated in  FIGS. 1 and 2 . The light amount adjuster  53  converts the received binary data into ON and OFF of the exposure beam L. That is, the light amount adjuster  53  turns off the exposure beam L for dots that represent white in the binary data, so as not to emit the light beam L, and the light amount adjuster  53  turns on the exposure beam L for dots that represent black in the binary data, so as to emit the light beam L to the image carrier  131 . It is noted that the light amount of the exposure beam L that is turned on for each of the dots representing black is adjusted based on an instruction from the light amount controller  54 . 
     The information on the screen and the binary data are input to the light amount controller  54 . In the first exemplary embodiment illustrated in  FIG. 3 , the image editing unit  51  and the data converter  52  are integrally configured, and the multi-level data cannot be taken out therefrom. 
     In an exposure control device  50 B according to a second exemplary embodiment illustrated in  FIG. 11 , the image editing unit  51  and the data converter  52  are separated, and the multi-level data can be taken out. Therefore, in the second exemplary embodiment, the multi-level data is input to the light amount controller  54 , and both of the screen data and the binary data are unnecessary. The second exemplary embodiment will be described later. Herein, the description on the exposure control device  50 A of the first exemplary embodiment illustrated in  FIG. 3  will be continued. 
     The light amount controller  54  includes the primary correction value table  61  and the correction magnification LUT  62 . The primary correction value table  61  and the correction magnification LUT  62  are created in advance and installed in the light amount controller  54 . 
     First, the primary correction value table  61  and the correction magnification LUT  62  will be described. 
       FIG. 4  is a diagram illustrating a flowchart of a procedure of creating the primary correction value table  61 . 
     The primary correction value table  61  is created for each image forming apparatus  10  at a preparatory stage before use of the image forming apparatus  10  starts or before factory shipment. 
     Herein, first, a uniform image, for example, an image having a dot percent of 60% is formed on a sheet (step S 01 ), and a density of each correction point is measured by the optical measuring unit  26  (step S 02 ). 
       FIG. 5  is a diagram illustrating the correction points. 
     Herein, as an example, thirty two (32) correction points are arranged at equal intervals within a length of one cycle of the developing roller  133   a  (see  FIG. 2 ) in a process direction (sheet transport direction) on the sheet. This configuration is adopted in order to consider correction of density nonuniformity caused by nonuniform rotation of the developing roller  133   a . In the example illustrated here, thirty two (32) correction points are also arranged at equal intervals in a width direction intersecting the process direction within an entire width of the sheet. In step S 02  of  FIG. 4 , the densities of the 32×32 correction points are measured by the optical measuring unit  26 . 
     In the image forming apparatus  10  illustrated in  FIG. 1 , the optical measuring unit  26  that measures the density of the image on the sheet is provided. Therefore, the uniform image is formed on the sheet and the densities are measured by the optical measuring unit  26 . Alternatively, the densities may be measured by a measuring unit separate from the image forming apparatus  10 . The uniform image may be, for example, a toner image directly formed on the intermediate transfer belt  14 . It is not necessary that the uniform image is an image formed on the sheet. In this case, it is necessary to use the measuring unit according to a place where the uniform image is formed, for example, a measuring unit that measures a density of the uniform toner image directly formed on the intermediate transfer belt  14 . 
     Returning to  FIG. 4 , the description will be continued. 
     In step S 03  of  FIG. 4 , a primary correction value of each correction point is calculated. 
       FIG. 6  is a diagram illustrating an example of the primary correction value table  61 . 
     The primary correction value table  61  is a table having 32 columns by 32 rows. Each cell corresponds to a respective one of the correction points. In each cell, the primary correction value of the corresponding one of the correction points is written. 
     Herein, the uniform image having the dot percent of 60% is formed, and the density of each correction point is measured. Therefore, each correction point has an expected value of the density corresponding to the dot percent of 60%. A pixel value measured at each correction point is ideally a pixel value representing the density as expected, but does not always match the expected value due to various error factors. The primary correction value in each cell of the primary correction value table  61  illustrated in  FIG. 6  represents a difference between the pixel value measured at the corresponding correction point and the expected value. For example, 7% in a cell at an upper left corner refers to that a pixel value measured at a correction point corresponding to that cell is smaller than the expected value of the cell and if the density is increased by 7%, the pixel value becomes the expected value. Similarly, 5% in a cell to the right of the cell at the upper left corner and −2% in a cell to the right of the cell having 5% respectively refer to that if the density is increased by 5%, the pixel value becomes the expected value and that if the density is decreased by 2%, the pixel value becomes the expected value. The same applies to the primary correction values in the other cells. For the purpose of simplification of the figure, the numerical values in the other cells are omitted. 
     The primary correction value table  61  created in this way is installed in the light amount controller  54  illustrated in  FIG. 3 . 
       FIG. 7  is a diagram illustrating an example of the correction magnification LUT  62 . 
     In  FIG. 7 , a horizontal axis represents multi-level data Cin (%) of each pixel represented in dot percent, and a vertical axis represents a correction magnification. The correction magnification LUT  62  is determined for each model of the image forming apparatus  10  or by a large number of experiments for plural models. Similar to the primary correction value table  61  illustrated in  FIG. 6 , the correction magnification LUT  62  is also installed in the light amount controller  54 . 
       FIG. 8  is a diagram illustrating a flowchart of a process executed on the light amount controller  54  of the exposure control device  50 A illustrated in  FIG. 3  when a user image is formed. 
     As described above, in the exposure control device  50 A of the first exemplary embodiment illustrated in  FIG. 3 , it is not possible to obtain the multi-level data representing Cin. Therefore, the exposure control device  50 A estimates Cin (step S 11 ). An arithmetic operation of estimating Cin in step S 11  will be described later. The description will be given with the assumption that Cin is already estimated. 
     The light amount controller  54  calculates the correction magnification based on the estimated Cin with reference to the correction magnification LUT  62  (step S 12 ). The light amount controller  54  reads the primary correction value with reference to the primary correction value table  61 , and multiplies the read primary correction value by the calculated correction magnification to calculate a light amount adjustment value (step S 13 ). The calculated light amount adjustment value is an example of a secondary correction value according to the present disclosure. The light amount controller  54  outputs the calculated light amount adjustment value to the light amount adjuster  53 . 
     The light amount adjuster  53  adjusts the light amount of the exposure beam L for each pixel according to the input light amount adjustment value. The image carrier  131  is exposed with the exposure beam L whose light amount is adjusted. 
     A method of calculating the correction magnification and a method of calculating the light amount adjustment value will be described. 
     The correction magnification LUT  62  illustrated in  FIG. 7  monotonically increases with respect to Cin (%) and has a correction magnification of 1.0 at a predetermined value (in this example, Cin=60%) or more. 
     It is assumed that the pixel value of the pixel overlapping the correction point at the upper left corner in  FIG. 5  is Cin=60% or a larger value larger than 60% when an actual user image is formed instead of forming the uniform image described above. At this time, for the pixel overlapping the correction point, the light amount of the exposure beam L is increased by 7% that is in the cell at the upper left corner of the primary correction value table  61  illustrated in  FIG. 6  from a predetermined reference light amount. When the pixel value of the pixel overlapping the correction point at the upper left corner in  FIG. 5  is Cin=35%, 7% is multiplied by a correction magnification of 0.5 read from the correction magnification LUT  62  in  FIG. 7 , and the light amount of the exposure beam L is larger by 7%×0.5=3.5% than the reference light amount, instead of 7%. When the pixel value of the pixel overlapping the correction point at the upper left corner in  FIG. 5  is Cin=10% or a value less than 10%, 7% is multiplied by a correction magnification of 0.0 read from the correction magnification LUT  62  in  FIG. 7 , and the light amount of the exposure beam L is increased by 0% (=7%×0.0) instead of 7%, that is, the exposure beam L having a light amount of the reference light amount is adopted. 
     It is assumed that Cin at a correction point that is to the right of the correction point at the upper left corner in  FIG. 5  has Cin=35% at in forming the user image. At this time, similar to the above, a primary correction value 5% of the corresponding correction point in  FIG. 6  is multiplied by the correction magnification of 0.5 read from the correction magnification LUT  62  in  FIG. 7 , and an exposure beam L having a light amount that is larger by 5%×0.5=2.5% than the reference light amount is adopted. 
     Similarly, it is assumed that a correction point that is second to the right of the correction point at the upper left corner has Cin=35% in forming the user image. At this time, similar to the above, a primary correction value −2% at the corresponding correction point in  FIG. 6  is multiplied by the correction magnification of 0.5 read from the correction magnification LUT  62  in  FIG. 7 , and an exposure beam L having a light amount that is smaller by 2%×0.5=1% than the reference light amount, that is, a light amount obtained by decreasing the reference light amount by 1% is adopted. 
     The light amount of the exposure beam L is adjusted for the pixel overlapping each correction point as described above. 
     Next, a method of adjusting a light amount of the exposure beam L for a pixel between two adjacent correction points will be described. 
     It is assumed that a light amount correction value relating to the pixel overlapping the correction point at the upper left corner in  FIG. 5  is 5%, and a light amount correction value relating to the pixel overlapping the correction point to the right of the pixel overlapping the correction point at the upper left corner is 2%, both of which are calculated based on the above-mentioned calculation method. At this time, for a pixel existing between the two pixels overlapping the two correction points, a light amount correction value is obtained by performing linear interpolation on 5% and 2%. That is, for the pixel in a center of the two pixels overlapping the two correction points, a light amount correction value (5%+2%)/2=3.5% is adopted. For a pixel at a position where a distance to the pixel whose light amount correction value is 5% and a distance to the pixel whose light amount correction value is 2% is 1:2, a light amount correction value (5%×2+2%)/3=4% is adopted. The same applies to pixels at the other positions. The pixels arranged in the width direction are described here. The same applies to pixels arranged in the process direction. 
     For a pixel at a position shifted from the correction points in both the width direction and the process direction, a light amount correction value is obtained by two-dimensional linear interpolation on the light amount correction values of four pixels overlapping four surrounding correction points. An algorithm of the two-dimensional linear interpolation has been well known, and the description thereof is omitted here. In the above description, the linear interpolation is adopted. It is noted that the linear interpolation does not have to be adopted. A higher-order interpolation may be adopted. 
     The uniform image described with reference to  FIG. 4  is a uniform image of Cin 60% for which the correction magnification LUT  62  is 1.0. That is, the uniform image is a uniform image of Cin for which the primary correction values illustrated in the primary correction value table  61  of  FIG. 6  and the light amount correction values calculated as described above are the same. It is assumed that the uniform image described with reference to  FIG. 4  is, for example, a uniform image of Cin=35%. In this case, the primary correction value is calculated in a similar manner. However, in this case, as a correction magnification LUT having effect equivalent to that of the correction magnification LUT  62  illustrated in  FIG. 7 , a correction magnification LUT in which a correction magnification is 2.0 when the pixel value of the user image is, for example, Cin=60% is created. Theoretically, (i) a case where a uniform image of Cin=60% or a value larger than 60% is formed and a correction magnification LUT in which the correction magnification is 1.0 at most is created and (ii) a case where a uniform image of a low Cin is created and a correction magnification LUT in which a correction magnification exceeding 1.0 appears is created are equivalent to each other with errors ignored. However, when the correction magnification exceeding 1.0 appears, an error is greatly amplified. The density nonuniformity of the image may be amplified without being corrected correctly. Therefore, in the exemplary embodiment, a uniform image of Cin=60% is created such that the correction magnification is at most 1.0. 
     Next, a method of estimating Cin in step S 11  of  FIG. 8  will be described. 
     Herein, Cin is estimated by counting the number of the white dots and the number of black dots in a region, having a size which is determined according to the screen used this time, around one correction point, and calculating a ratio of the white dots and the black dots. 
       FIG. 9  is a diagram illustrating an image of the region determined according to the screen. 
     The region where the number of the white dots and the number of the black dots are counted for Cin estimation is switched according to the screen. For example, for a 212 lpi screen at a 45-degree screen angle that is used in general, when a lighting resolution is 2,400 dpi, a region of a multiple of 8 lines (here, 16 lines that is twice 8 lines) is selected. 
     This is based on the following calculation formulas. That is, a screen at a 45-degree screen angle has a repetition period of square root of 2 times, that is, about 1.4 times in a 0-degree direction. The 212 lpi screen at the 45-degree screen angle has the same repetition period in the 0-degree direction as a 300 lpi screen at a 0-degree screen angle. The term “212 lines per inch (lpi)” refers to 212 dots in 1 inch (≈25.4 mm). That is, dots of 0.12 mm (≈25.4 mm/212) are arranged. In a 300 lpi screen, dots of 0.085 mm (≈25.4 mm/300) are arranged. Herein, one dot of an image output at 2,400 dpi is 25.4/2400≈0.011 mm Therefore, the 300 lpi screen at the 0-degree screen angle repeats in a unit of (25.4 mm/300)/(25.4/2400)=8 dots. Then, for the 212 lpi screen at the 45-degree screen angle, 8×2=16 lines in the process direction are adopted as a region for Cin estimation. In the width direction, a wide 127-dot region is adopted. When a region having the same length in the process direction as that in the width direction is adopted, estimation errors of Cin decrease, but a huge memory capacity is required. Therefore, a region is set to be twice as large as the number of repeated dots. 
     For a 190 lpi screen at a 45-degree screen angle, a region having a multiple of 9 (here 9×2=18 lines) is similarly adopted. This region has 127 dots in the width direction. 
     A screen at a screen angle other than 0 degree or 45 degrees has no repetition period with a small number of dots in the 0-degree direction. Therefore, it is not necessary to pay particular attention to the number of repeated dots when determining the region. 
     In this way, the region where the number of the white dots and the black dots of the binary data is counted is set around each correction point, and the number of data representing the white dots and the number of data representing the black dots in the region are counted. For example, when a percentage of the white dots is 40% and a percentage of the black dots is 60%, it is estimated that Cin=60%. Further, for example, when the percentage of white dots is 80% and the percentage of the black dots is 20%, it is estimated that Cin=20%. 
       FIG. 10  is a diagram illustrating estimation errors of Cin relating to the types of the screen and the widths of the region in the process direction. 
     For the 212 lpi screen at the 45-degree screen angle, when the region of 16 lines is selected as in the calculation formula described above, the estimation errors of Cin are reduced compared to selecting a region of 17 lines or 18 lines. 
     Further, for a 190 lpi screen at a 45-degree screen angle, when the region of 18 lines is selected, the estimation errors of Cin are reduced compared to selecting the region of 16 lines or 17 lines. 
     A 205 lpi screen at a 20-degree screen angle or a 70-degree screen angle, and a 185 lpi screen at a 12-degree screen angle or a 67-degree screen angle have no repetition period with a small number of dots in the 0-degree direction. Therefore, the estimation errors of Cin are at the same level regardless of which region of 16 lines, 17 lines, or 18 lines is selected. 
     Herein, the example has been described in which information on the screen to be used this time is obtained and the region where the number of the white dots and the black dots are counted is set according to the screen. When the screen to be used is determined in advance and initialized, a region for the initialized screen may be always adopted. 
     In this way, when Cin is estimated in step S 11  of  FIG. 8 , as described above, the correction magnification corresponding to the estimated Cin is calculated with reference to the correction magnification LUT  62  illustrated in  FIG. 7  (step S 12 ). Then, the light amount adjustment value is calculated with reference to the primary correction value table  61  illustrated in  FIG. 6 . The light amount of the exposure beam L emitted from the exposure unit  12  is adjusted according to the light amount adjustment value. 
       FIG. 11  is a block diagram illustrating a configuration of an exposure control device  50 B according to the second exemplary embodiment of the present disclosure. Herein, description will focus on differences from the exposure control device  50 A of the first exemplary embodiment illustrated in  FIG. 3 . 
     In the exposure control device  50 A of the first exemplary embodiment illustrated in  FIG. 3 , the information on the screen and the binary data are input to the light amount controller  54 , the region is set according to the screen, and Cin is estimated by counting the number of the white dots and the number of the black dots represented by the binary data in the region. 
     On the other hand, the exposure control device  50 B of the second exemplary embodiment illustrated in  FIG. 11  can obtain multi-level data representing Cin, and the multi-level data is input to the light amount controller  54 . In the light amount controller  54 , the input Cin is used (at step S 11  in  FIG. 8 ) as it is without performing the above Cin estimation, the correction magnification is calculated (at step S 12  in  FIG. 8 ), and then the light amount correction value is calculated (at step S 13  in  FIG. 8 ). 
     Similar to the exposure control device  50 A of the first exemplary embodiment, the exposure control device  50 B of the second exemplary embodiment adjusts the light amount of the exposure beam L emitted from the exposure unit  12  without adjusting the value of Cin on the data (for example, rewriting Cin=35 as Cin=38). Therefore, it is possible to adjust the light amount more finely than in Japanese Patent No. 5825862 in which the value of Cin is adjusted on the data. 
     The tandem image forming apparatus for forming a color image has been described as an example. It is noted that the present disclosure is applicable to a monochrome printer and the like. 
     The foregoing description of the exemplary embodiments of the present disclosure has been provided for the purposes of illustration and description. It is not intended to be exhaustive or to limit the disclosure to the precise forms disclosed. Obviously, many modifications and variations will be apparent to practitioners skilled in the art. The embodiments were chosen and described in order to best explain the principles of the disclosure and its practical applications, thereby enabling others skilled in the art to understand the disclosure for various embodiments and with the various modifications as are suited to the particular use contemplated. It is intended that the scope of the disclosure be defined by the following claims and their equivalents.