Patent Publication Number: US-11644765-B2

Title: Image forming apparatus capable of correcting density unevenness of an image

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is based on and claims priority under 35 USC 119 from Japanese Patent Application No. 2021-137640 filed Aug. 25, 2021. 
     BACKGROUND 
     (i) Technical Field 
     The present disclosure relates to an image forming apparatus. 
     (ii) Related Art 
     Japanese Unexamined Patent Application Publication No. 2012-108454 discloses an image forming apparatus that determines, on the basis of an output signal of a density sensor that detects density variations occurred in an output image in a subscanning direction and an output signal of a drum-period detection sensor, a periodic pattern of a sine wave representing density variations in the subscanning direction and performs density correction by using the periodic pattern. 
     Japanese Unexamined Patent Application Publication No. 2012-255834 discloses an image processing apparatus that creates and stores beforehand a correction table in which correction amounts for correcting density variations that occur due to a device employing an electrophotographic system in such a manner as to perform a periodic movement when an image is formed by using this device are each calculated so as to correspond to a rotation phase, the image processing apparatus being configured to perform density correction by using a correction amount based on the correction table and output the image when the image processing apparatus forms an image. 
     SUMMARY 
     Aspects of non-limiting embodiments of the present disclosure relate to providing an image forming apparatus capable of correcting irregular density unevenness other than periodic density unevenness that occur in an image, which is to be formed, in a subscanning direction and reducing the amount of data required to be stored compared with the case of using a correction table in which correction amounts for correcting all the density unevennesses in the subscanning direction are each stored in association with a corresponding position in the subscanning direction or a corresponding rotation phase of a rotating body. 
     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 image forming apparatus including: an output section that forms an electrostatic latent image onto an image carrier by using light emitted by a light source and outputs an image onto a recording medium by developing the formed electrostatic latent image; a memory that stores a sinusoidal set value representing a correction amount for correcting periodic density variations that occur in an image, which is to be formed, in a subscanning direction and that are caused by a rotating body, and a correction table in which correction amounts for correcting density variations that occur in an image, which is to be formed, in the subscanning direction and that are not caused by a rotating body are each stored in association with a corresponding position in the subscanning direction; and a processor configured to: calculate a first correction amount corresponding to a rotation phase of a rotating body included in the output section on a basis of the sinusoidal set value and retrieve a second correction amount corresponding to a position in the subscanning direction from the correction table when an image is formed in the output section; and perform, by using the calculated first correction amount and the retrieved second correction amount, correction of a density of an image that is formed onto a recording medium. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Exemplary embodiments of the present disclosure will be described in detail based on the following figures, wherein: 
         FIG.  1    is a diagram illustrating the configuration of an image forming apparatus according to an exemplary embodiment of the present disclosure; 
         FIG.  2    is a diagram illustrating the positional relationship between a photoconductor roller and a developing roller; 
         FIG.  3    is a diagram illustrating directions that relate to an image to be formed and to the arrangement of the image forming apparatus; 
         FIG.  4    is a block diagram illustrating the hardware configuration of a controller that controls the operation of the image forming apparatus according to the exemplary embodiment of the present disclosure; 
         FIG.  5    is a block diagram illustrating the functional configuration of the controller illustrated in  FIG.  4   ; 
         FIG.  6    is a flowchart illustrating an operation of a density correction unit when the density correction unit creates a sinusoidal parameter and a correction table for density correction; 
         FIG.  7    is a diagram illustrating an example of a waveform of a result obtained by applying a sine wave to a density variation profile detected by a density sensor; 
         FIG.  8    is a diagram illustrating an example of a density variation profile obtained by averaging density variation profiles from the density sensor on the basis of their positions with respect to a top-of-page signal; 
         FIG.  9 A  and  FIG.  9 B  respectively illustrate a density variation profile representing a density variation amount at each position in a subscanning direction and a density correction amount profile in which density variations are canceled by reversing the positive and negative components in  FIG.  9 A ; 
         FIG.  10    is a table illustrating examples of combinations of a direction of density unevenness, the density of a correction target, a correction-amount storing method, and a correction method when density unevenness correction is performed; 
         FIG.  11    is a flowchart illustrating processing that is performed when an image is actually formed by using a correction amount for density correction; 
         FIG.  12    is a flowchart illustrating an operation of the density correction unit when density correction of periodic density unevenness in a solid density in the subscanning direction is performed by using a correction table; 
         FIG.  13    is a diagram illustrating an example of a density variation profile obtained by the density sensor; 
         FIG.  14    is a diagram illustrating the state of the density variation profile illustrated in  FIG.  13    being divided by a period T of the photoconductor roller and averaged; 
         FIG.  15 A  and  FIG.  15 B  respectively illustrate a density variation profile representing density variation amounts each corresponding to a rotation phase of the photoconductor roller and a density correction amount profile in which density variations are canceled by reversing the positive and negative components in  FIG.  15 A ; 
         FIG.  16    is a table illustrating examples of combinations of a direction of density unevenness, the density of a correction target, a correction-amount storing method, and a correction method at the time of performing density unevenness correction such as density correction of periodic density unevenness in a solid density in the subscanning direction that is performed by using a correction table; 
         FIG.  17    is a block diagram illustrating an example of the configuration of the density correction unit; 
         FIG.  18    is a diagram illustrating an example of an operation screen that prompts a user as to whether the user selects a first density correction method that gives priority to reducing density unevenness in halftones or a second density correction method that gives priority to reducing density unevenness near a highest density; 
         FIG.  19    is a diagram illustrating the operation of the density correction unit when the first density correction method that gives priority to reducing density unevenness in halftones is selected; and 
         FIG.  20    is a diagram illustrating the operation of the density correction unit when the second density correction method that gives priority to reducing density unevenness near the solid density is selected. 
     
    
    
     DETAILED DESCRIPTION 
     Exemplary embodiments of the present disclosure will be described in detail below with reference to the drawings. 
       FIG.  1    is a diagram illustrating the configuration of an image forming apparatus  10  according to an exemplary embodiment of the present disclosure. 
     As illustrated in  FIG.  1   , the image forming apparatus  10  includes image forming units  14 K,  14 C,  14 M, and  14 Y, an intermediate transfer belt  16 , a sheet tray  17 , a sheet transport path  18 , a fixing unit  19 , and a controller  20 . The image forming apparatus  10  has a printer function that prints image data, which is received from a personal computer (not illustrated) or the like. 
     First, an overview of the image forming apparatus  10  will be described. The controller  20  is positioned in an upper portion of the image forming apparatus  10 . The controller  20  performs image processing such as gradation correction and resolution correction on image data input from a personal computer (not illustrated) or the like via a network line, such as a LAN, and then outputs the image data to the image forming units  14 . 
     The four image forming units  14 K,  14 C,  14 M, and  14 Y are arranged below the controller  20  such that each of the four image forming units  14 K,  14 C,  14 M, and  14 Y corresponds to one of the colors of color images. In the present exemplary embodiment, the four image forming units  14 K,  14 C,  14 M, and  14 Y that correspond to black (K), cyan (C), magenta (M), and yellow (Y), respectively, are horizontally arranged along the intermediate transfer belt  16  in such a manner as to be spaced apart from one another by a certain distance. The intermediate transfer belt  16  serves as an intermediate transfer body and moves along a circular path in the direction of arrow A in  FIG.  1   . The four image forming units  14 K,  14 Y,  14 M, and  14 C sequentially form toner images of their respective colors on the basis of image data input from the controller  20  and transfer (in a first transfer process) these toner images onto the intermediate transfer belt  16  at the timing at which the toner images are superposed with one another. Note that the image forming units  14 K,  14 C,  14 M, and  14 Y are not limited to being arranged in the order of colors black (K), cyan (C), magenta (M), and yellow (Y) and may be in any order (e.g., yellow (Y), magenta (M), cyan (C), and black (K)). 
     The sheet transport path  18  is disposed below the intermediate transfer belt  16 . A recording sheet  32  that is supplied from the sheet tray  17  is transported along the sheet transport path  18 , and the toner images of the different colors, which have been transferred to the intermediate transfer belt  16  in such a manner as to be superposed with one another, are collectively transferred (in a second transfer process) onto the recording sheet  32 . Then, the transferred toner images are fixed onto the recording sheet  32  by the fixing unit  19 , and the recording sheet  32  is ejected to the outside in the direction of arrow B. 
     The configuration of each component of the image forming apparatus  10  will now be described in further detail. 
     The controller  20  performs predetermined image processing such as shading correction, lightness/color space conversion, and gamma correction on image data input thereto. Note that, in the case where the input image data contains data components of, for example, red (R), green (G), and blue (B) each of which is composed of eight bits, these data components are converted into, through the image processing performed by the controller  20 , document-color-material-gradation data components, each of which has one of four colors of black (K), cyan (C), magenta (M), and yellow (Y) and each of which is composed of 8 bits. 
     The image forming units (image forming units)  14 K,  14 C,  14 M, and  14 Y are arranged side by side in the horizontal direction in such a manner as to be spaced apart from one another by a certain distance, and the configurations of the image forming units  14 K,  14 C,  14 M, and  14 Y are substantially similar to one another except for the colors of images formed thereby. Accordingly, the image forming unit  14 K will be described below. Note that the configurations of the image forming units  14  are distinguished from one another by adding the letters K, C, M, and Y to the reference signs. 
     The image forming unit  14 K includes an exposure unit  140 K that radiates light onto an image forming device  150 Y in accordance with image data, which is input from the controller  20 , and the image forming device  150 Y on which an electrostatic latent image is formed by a laser beam that is caused to scan the image forming device  150 Y by the exposure unit  140 K. 
     The exposure unit  140 K exposes a photoconductor roller  152 K of the image forming device  150 Y to light by radiating a laser beam that corresponds to black (K) image data onto the photoconductor roller  152 K so as to form an electrostatic latent image onto the photoconductor roller  152 K. Note that the exposure unit  140 K includes a plurality of bar-shaped LED print heads (LPHs) in each of which a plurality of LEDs, which are light emitting elements, are arranged. Details of the configuration of the exposure unit  140 K will be described later. 
     The image forming device  150 Y includes the photoconductor roller  152 K that performs a rotational movement in the direction of arrow A at a predetermined rotational speed, a charging device  154 K serving as a charging unit that uniformly charges a surface of the photoconductor roller  152 K, a developing device  156 K that develops an electrostatic latent image formed on the photoconductor roller  152 K, and a cleaning device  158 Y. The photoconductor roller  152 K is an image carrier that has a tubular shape and that holds an image, which has been developed with a developer such as toner, and is uniformly charged by the charging device  154 K, and an electrostatic latent image is formed on the photoconductor roller  152 K by the laser beam radiated from the exposure unit  140 K. An electrostatic latent image formed on the photoconductor roller  152 K is developed by the developing device  156 K with a developer such as black (K) toner and transferred onto the intermediate transfer belt  16 . Note that residual toner, paper dust, and the like that remain on the photoconductor roller  152 K after a process of transferring a toner image (a developer image) has been executed are removed by the cleaning device  158 Y. 
     Similar to the image forming unit  14 K, the image forming unit  14 C includes a photoconductor roller  152 C and a developing device  156 C and forms a cyan (C) toner image. The image forming unit  14 M includes a photoconductor roller  152 M and a developing device  156 M and forms a magenta (M) toner image. The image forming unit  14 Y includes a photoconductor roller  152 Y and a developing device  156 Y and forms a yellow (Y) toner image. These toner images of the different colors are transferred onto the intermediate transfer belt  16 . 
     The intermediate transfer belt  16  is stretched by a drive roller  164 , idle rollers  165 ,  166 , and  167 , a backup roller  168 , and an idle roller  169  with a certain tension and is driven so as to rotate in the direction of arrow A at a predetermined speed as a result of the drive roller  164  being driven by a drive motor (not illustrated) so as to rotate. The intermediate transfer belt  16  has the form of an endless belt obtained by, for example, forming a flexible film made of a synthetic resin, such as a polyimide, into a belt-like shape and joining the two ends of the synthetic resin film, which has a belt-like shape, to each other by welding or the like. 
     First transfer rollers  162 K,  162 C,  162 M, and  162 Y are arranged at positions on the intermediate transfer belt  16  at which the first transfer rollers  162 K,  162 C,  162 M, and  162 Y face the image forming units  14 K,  14 C,  14 M, and  14 Y, respectively. Toner images of the different colors that are formed on the photoconductor rollers  152 K,  152 C,  152 M, and  152 Y are transferred onto the intermediate transfer belt  16  in such a manner as to be superposed with one another by the first transfer rollers  162 . Note that residual toner that remains on the intermediate transfer belt  16  is removed by a cleaning blade or a brush of a belt cleaning device  189  that is disposed at a position downstream from a second transfer position. 
     A density sensor  170  is disposed in the vicinity of the intermediate transfer belt  16 . The density sensor  170  is a density detection unit that detects the density of a toner image transferred to the intermediate transfer belt  16 . 
     A sheet feed roller  181  that picks up the recording sheet  32  from the sheet tray  17 , a first pair of rollers  182 , a second pair of rollers  183 , and a third pair of rollers  184  each pair of which is used for transporting sheets, and registration rollers  185  that transport the recording sheet  32  to the second transfer position at a predetermined timing are arranged on the sheet transport path  18 . 
     A second transfer roller  186  that is pressed into contact with the backup roller  168  is disposed at the second transfer position on the sheet transport path  18 , and toner images of the different colors, which have been transferred to the intermediate transfer belt  16  in such a manner as to be superposed with one another, are transferred in the second transfer process onto the recording sheet  32  with a press-contact force and an electrostatic force exerted by the second transfer roller  186 . The recording sheet  32 , to which the toner images of the different colors have been transferred, is transported to the fixing unit  19  by a transport belt  187  and a transport belt  188 . 
     The fixing unit  19  performs a heat treatment and a pressure treatment on the recording sheet  32 , to which the toner images of the different colors have been transferred, so as to cause the toners to melt and become fixed onto the recording sheet  32 . 
     Note that the developing device  156 K includes a developing roller (developer transport unit)  157 K that has a tubular shape, and the developing roller  157 K transports the developer to the photoconductor roller  152 K by performing a rotational movement so as to form a developer image onto the photoconductor roller  152 K. Similarly, in the image forming units  14 C,  14 M, and  14 Y, which form images of the other colors, the developing devices  156 C,  156 M, and  156 Y each include a developing roller  157 C,  157 M and  157 Y. 
     The image forming apparatus  10  of the present exemplary embodiment having a configuration such as that described above employs an electrophotographic system and forms an image onto a recording medium such as a printing sheet. The image forming units  14 , the intermediate transfer belt  16 , the fixing unit  19 , and so forth that have been described above form an output section, and this output section forms electrostatic latent images onto the photoconductor rollers  152 , each of which is an image carrier, by light radiated from a light source and outputs an image onto a recording medium by developing the formed electrostatic latent images. 
     However, since the image forming apparatus  10  of the present exemplary embodiment performs image formation by using rotating bodies such as the photoconductor rollers  152  and the developing rollers  157 , periodic density unevenness (density variations) may sometimes occur in a subscanning direction, which is a sheet-transport direction. 
     For example,  FIG.  2    illustrates the positional relationship between one of the photoconductor rollers  152  and the corresponding developing roller  15 . 
     As illustrated in  FIG.  2   , the photoconductor roller  152  and the developing roller  157  are arranged in such a manner as to face each other with a predetermined space (gap) formed therebetween. The developing roller  157  holds the developer on its surface by a magnetic force of a magnet that is disposed within the developing roller  157  and transports the developer, which is held on the surface thereof, to the gap between the photoconductor roller  152  and the developing roller  157  by performing a rotational movement so as to develop an electrostatic latent image formed on the surface of the photoconductor roller  152  into a visible image. 
     However, in the case where the rotation axis of the photoconductor roller  152  or the rotation axis of the developing roller  157  is displaced from and eccentric to an ideal rotation axis, the gap between the photoconductor roller  152  and the developing roller  157  changes periodically. A similar problem occurs in the case where the photoconductor roller  152  and the developing roller  157  are not arranged so as to be completely parallel to each other. In addition, a similar problem occurs also in the case where the shape of the photoconductor roller  152  or the shape of the developing roller  157  is distorted or deformed. 
     In an image that is formed with the occurrence of such a problem, periodic density unevenness may sometimes occur in the subscanning direction. 
     Directions that relate to an image to be formed and to the arrangement of the image forming apparatus  10  will now be described with reference to  FIG.  3   . As illustrated in  FIG.  3   , a direction in which each of the exposure units  140  causes a laser beam to scan, that is, the longitudinal direction of each of the photoconductor rollers  152 , will hereinafter be referred to as a main scanning direction. In addition, a direction that is perpendicular to the main scanning direction, that is, a sheet-transport direction in which a printing sheet or the like is transported will hereinafter be referred to as the subscanning direction. 
       FIG.  4    illustrates the hardware configuration of the controller  20  that controls the operation of the image forming apparatus  10  of the present exemplary embodiment. 
     As illustrated in  FIG.  4   , the controller  20  includes a CPU  41 , memory  42 , a storage device  43  such as a hard disk drive, a communication interface  44  that performs transmission and reception of data with, for example, an external device via a network, and a user interface (hereinafter abbreviated to “UI”) device  45  that includes a touch panel or a liquid crystal display and a keyboard. These components are connected to one another via a control bus  46 . 
     The CPU  41  is a processor that controls the operation of the controller  20  by performing predetermined processing on the basis of a control program stored in the memory  42  or the storage device  43 . Note that, in the present exemplary embodiment, although the CPU  41  is configured to read and run a control program stored in the memory  42  or the storage device  43 , the program may be provided to the CPU  41  by being stored in a storage medium such as a compact disc read-only memory (CD-ROM). 
       FIG.  5    is a block diagram illustrating the functional configuration of the controller  20  illustrated in  FIG.  4    that is constructed by running the above-mentioned control program. 
     As illustrated in  FIG.  5   , the controller  20  includes a density correction unit  21 , a correction table storing unit  22 , and a sinusoidal parameter storing unit  23 . 
     The density correction unit  21  detects density unevenness occurred in an output image on the basis of density information such as a density value detected by the density sensor  170  and adjusts the light exposure of each of the exposure units  140  or changes a pixel value used when an image is formed so as to suppress the detected density unevenness. Note that, the density correction unit  21  determines a position in an image at which such density correction is performed on the basis of rotation phase information such as a Z-phase signal of each of the photoconductor rollers  152 , rotation phase information such as a Z-phase signal of each of the developing rollers  157 , a top-of-page signal, and a start-of-scan signal. 
     Here, if correction of density unevenness is performed by using a correction table in which correction amounts are each stored in association with a corresponding position in the subscanning direction, finer density variations may be accurately corrected. However, in the case of correcting all the density unevennesses in the subscanning direction by using such a correction table, it is necessary to store beforehand a correction table corresponding to the rotation phase of each of the photoconductor rollers  152 , a correction table corresponding to the rotation phase of each of the developing rollers  157 , a correction table corresponding to each page position, and so forth. Thus, this case has an undesirable effect of increasing the amount of data required to be stored. 
     In the case of correcting density unevenness by using a correction amount represented by a sinusoidal parameter, the accuracy with which the density unevenness is corrected may sometimes be lower than that in the case of correcting density unevenness by using a correction table. In addition, it is difficult to correct more irregular density unevenness occurred due to collision between a sheet and a member by using a sinusoidal parameter. 
     Accordingly, in the present exemplary embodiment, density correction using a sinusoidal parameter (a sinusoidal set value) is performed on periodic density variations that occur in the subscanning direction due to a rotating body, and density correction using a correction table is performed on density variations that occur in the subscanning direction not due to a rotating body. 
     The sinusoidal parameter storing unit  23  stores a sinusoidal parameter (a sinusoidal set value) representing a correction amount for correcting periodic density variations that occur in an image, which is to be formed, in the subscanning direction and that are caused by a rotating body. 
     The correction table storing unit  22  stores a correction table in which correction amounts for correcting density variations that occur in an image, which is to be formed, in the subscanning direction and that are not caused by a rotating body are each stored in association with a corresponding position in the subscanning direction. 
     The density correction unit  21  extracts a sinusoidal parameter representing periodic variations in density unevenness that is detected on the basis of a density value obtained by the density sensor  170  and stores a sinusoidal parameter that has a characteristic of canceling the extracted sinusoidal parameter in the sinusoidal parameter storing unit  23  as a correction amount for the correcting density unevenness. 
     In addition, the density correction unit  21  creates a correction table in which correction amounts for correcting density variations other than periodic density variations in density unevenness that is detected on the basis of a density value obtained by the density sensor  170  are each stored in association with a corresponding position in the subscanning direction and stores the correction table into the correction table storing unit  22 . 
     When an image is formed in the image output section, the density correction unit  21  calculates, on the basis of a sinusoidal parameter, a first correction amount that corresponds to the rotation phase of a rotating body such as each of the photoconductor rollers  152  or each of the developing rollers  157  and obtains a second correction amount that corresponds to a position in the subscanning direction from the correction table stored in the correction table storing unit  22 . 
     When an image is formed onto a recording medium, the density correction unit  21  performs density correction on the image that is formed onto the recording medium by using the calculated first correction amount and the obtained second correction amount. 
     Note that, regarding density correction for correcting density unevenness, the density correction that is performed in the case of correcting density variations that occur near a highest density and the density correction that is performed in the case of correcting density variations in halftones are different from each other. 
     Thus, in order to reduce the amount of data given a top priority to be stored, density corrections may be performed, for periodic density unevenness in the subscanning direction that is caused by a rotating body, on both density variations that occur near the highest density and density variations in halftones by using a correction amount using a sinusoidal parameter. 
     More specifically, the density correction unit  21  performs density correction using the first correction amount, which is calculated on the basis of a sinusoidal parameter, both in the case of correcting density variations in halftones that occur in the subscanning direction due to a rotating body and in the case of correcting density variations that occur near the highest density. 
     When the density correction unit  21  performs correction of a halftone density by using the first correction amount, the density correction unit  21  performs the density correction by changing a pixel value in an image to be formed, and when the density correction unit  21  performs density correction near the highest density by using the first correction amount, the density correction unit  21  performs the density correction by changing the light exposure of each of the exposure units  140 . 
     In the case where it is desired to perform more accurate density correction on density variations that occur near the highest density, a correction amount for correcting density variations that occur near the highest density among periodic density variations that occur in an image, which is to be formed, in the subscanning direction and that are caused by a rotating body may be stored in the correction table, which is stored in the correction table storing unit  22 , in association with the rotation phase of the rotating body. 
     In this case, the density correction unit  21  performs density correction using the first correction amount, which is calculated on the basis of a sinusoidal parameter, in the case of correcting density variations in halftones that occur in the subscanning direction due to a rotating body and performs density correction using the second correction amount, which is retrieved from the correction table in accordance with the rotation phase of the rotating body, in the case of correcting density variations that occur near the highest density. 
     When the density correction unit  21  performs density correction using the first correction amount, the density correction unit  21  performs the density correction by changing a pixel value in an image to be formed, and when the density correction unit  21  performs density correction on density variations caused by a rotating body by using the second correction amount, the density correction unit  21  performs the density correction by changing the light exposure of each of the exposure units  140  in the image output section. 
     Note that the rotating body that causes density unevenness to occur in an image, which is to be formed, in the subscanning direction is specifically at least one of the photoconductor rollers  152  or at least one of the developing rollers  157 . 
     The operation of the density correction unit  21  when the density correction unit  21  performs density correction in the image forming apparatus  10  of the present exemplary embodiment will now be described in detail with reference to the drawings. 
     The flowchart in  FIG.  6    illustrating an operation of the density correction unit  21  when the density correction unit  21  creates a sinusoidal parameter and a correction table for density correction. 
     First, in step S 101 , the image output section forms a patch image having a density near the highest density (Cin≈100%) (hereinafter referred to as a “solid density”) onto the intermediate transfer belt  16 , and the density sensor  170  detects the density of the patch image, so that the density correction unit  21  obtains a density variation profile that is continuous in the subscanning direction, which is the sheet-transport direction. 
     Here, the density sensor  170  may be configured to detect not only the density of an unfixed image on the intermediate transfer belt  16  but also the density of an unfixed image on each of the photoconductor rollers  152 . The density sensor  170  radiates light onto an unfixed image on the intermediate transfer belt  16  or an unfixed image on each of the photoconductor rollers  152  and detects the intensity of reflected light. Note that the intensity of light reflected by an image fixed to a sheet may be detected by an in-line sensor or a scanner. 
     Note that the term “Cin” refers to a gradation area percentage expressing gradation in terms of the amount of toner when the maximum usable amount of toner for a certain color is 100%. In other words, the phrase “Cin=100%” refers to the highest density. In addition, the phrase “near the highest density” refers to Cin within a range of 80% to 100%. 
     Next, in step S 102 , the density correction unit  21  creates a sinusoidal parameter for density correction on the basis of the obtained density variation profile. 
     More specifically, the density correction unit  21  performs, on the obtained density variation profile, an inner product calculation of a sine wave and a cosine wave of a period set in accordance with the peripheral length of a rotating body, such as each of the photoconductor rollers  152  or each of the developing rollers  157 , or the peripheral speed ratio between members and a higher-order component of the period. The phase and the amplitude when the sine wave is applied to the density variation profile may be obtained from the inner product result.  FIG.  7    illustrates an example of a waveform of a result obtained by applying a sine wave to a density variation profile in the manner described above. 
     The density correction unit  21  calculates the phase difference from the distance between the start of the density variation profile and a Z-phase signal of the rotating body and the period and converts the obtained phase into a phase with respect to the Z phase of the rotating body. Note that the inner product result may be more exactly obtained by using the method of least squares instead of performing an inner product calculation. 
     Then, the density correction unit  21  shifts the phase by only π with respect to the calculated phase and amplitude, and the density correction unit  21  corrects the amplitude in accordance with the input/output response at the time of performing density correction and creates a sinusoidal parameter for density correction. The created sinusoidal parameter is stored in the sinusoidal parameter storing unit  23 . 
     Next, in step S 103 , the image output section forms a patch image having a halftone density (e.g., Cin≈25%, 50%, or 75%) onto the intermediate transfer belt  16 , and the density sensor  170  detects the density of the patch image, so that the density correction unit  21  obtains a density variation profile that is continuous in the subscanning direction, which is the sheet-transport direction. 
     When the halftone density variation profile is obtained, a patch image may be formed while performing density correction by using the sinusoidal parameter obtained in step S 102 . 
     Then, in step S 104 , the density correction unit  21  creates a sinusoidal parameter for correcting a halftone density on the basis of the halftone density variation profile obtained in step S 103 . The specific method of creating the sinusoidal parameter is the same as the method described in step S 102 . 
     Next, in step S 105 , the image output section forms a patch image having the solid density near the highest density onto the intermediate transfer belt  16 , and the density sensor  170  detects the density of the patch image, so that the density correction unit  21  obtains a density variation profile that is continuous in the subscanning direction, which is the sheet-transport direction. 
     Note that, in step S 105 , a density variation profile for correcting density unevenness caused by another factor that is different from periodic density unevenness caused by a rotating body is obtained. An example of a correction target is impulse binding or the like that is caused by, for example, vibration generated when a sheet abuts against a member. 
     Also in step S 105 , a patch image having the solid density is formed, and a density variation profile is obtained. However, the density variation profile in this step may be considered as, for example, a portion of a signal having a period starting from a top-of-page signal to the top-of-page signal of the next sheet. 
     The density correction unit  21  may determine the position of the density variation profile with respect to the top-of-page signal and may obtain a plurality of density variation profiles by repeatedly forming a patch image. 
     Note that, when the density variation profile is obtained in step S 105 , a patch image is formed in a state where density correction of periodic density unevenness has been performed by using the sinusoidal parameters created in step S 102  and step S 104 . 
     Subsequently, the density correction unit  21  averages the obtained density variation profiles on the basis of the positions with respect to the top-of-page signal.  FIG.  8    illustrates an example of a density variation profile obtained in the manner described above. 
     Then, in step S 106 , the density correction unit  21  determines a density correction amount by reversing the positive and negative components of the density variation profile obtained in the manner described above and creates a correction table on the basis of the density correction amount. 
       FIGS.  9 A and  9 B  illustrate the case of determining a density correction amount by reversing the positive and negative components of a density variation profile.  FIG.  9 A  and  FIG.  9 B  respectively illustrate a density variation profile representing a density variation amount at each position in the subscanning direction and a density correction amount profile in which density variations are canceled by reversing the positive and negative components in  FIG.  9 A . 
     Note that the density correction unit  21  performs the density correction by adjusting the light exposure of each of the exposure units  140 , and thus, the values stored in the actual correction table are multiplied by the sensitivity at the time of changing the light exposure. 
     Next, in step S 107 , the image output section forms a patch image having a halftone density onto the intermediate transfer belt  16 , and the density sensor  170  detects the density of the patch image, so that the density correction unit  21  obtains a halftone density variation profile that is continuous in the subscanning direction, which is the sheet-transport direction. Note that the method of obtaining the density variation profile is similar to the method described in step S 105  except with regard to the density of a patch image to be formed. 
     Note that, when the density variation profile is obtained in step S 107 , a patch image is formed in a state where density correction of density unevenness has been performed by using the sinusoidal parameters created in step S 102  and step S 104  and the correction table created in step S 106 . 
     Next, in step S 108 , the density correction unit  21  determines a density correction amount by reversing the positive and negative components of the obtained halftone density variation profile and creates a correction table on the basis of the density correction amount. Here, the specific method of creating the correction table is similar to the above-described method described in step S 106 . However, a density correction amount stored in the correction table is converted not into a correction amount for adjusting light exposure but into a correction amount for changing a pixel value in an image to be formed. 
     Next, in step S 109 , a density variation profile of the solid density in the main scanning direction, which is perpendicular to the subscanning direction, is obtained. Here, the target of density correction is density unevenness in the main scanning direction that repeatedly occurs for each page due to, for example, uneven wear of at least one of the photoconductor rollers  152 , a cutting mark formed on at least one of the photoconductor rollers  152 , unevenness in the light intensity of at least one of the exposure units  140 . 
     Note that, when the density variation profile is obtained in step S 107 , a patch image is formed in a state where density correction of density unevenness has been performed by using the sinusoidal parameters created in step S 102  and step S 104  and the correction tables created in step S 106  and step S 108 . 
     Then, in step S 110 , the density correction unit  21  determines a density correction amount by reversing the positive and negative components of the obtained density variation profile of the solid density and creates a correction table on the basis of the density correction amount. Here, the specific method of creating the correction table is similar to the above-described method described in step S 106 . In addition, regarding a density correction amount that is stored in the correction table, similar to step S 106 , a correction amount for adjusting light exposure is stored. 
     Finally, in step S 111 , a halftone density variation profile in the main scanning direction, which is perpendicular to the subscanning direction, is obtained. 
     Then, in step S 112 , the density correction unit  21  determines a density correction amount by reversing the positive and negative components of the obtained halftone density variation profile and creates a correction table on the basis of the density correction amount. Here, the specific method of creating the correction table is similar to the above-described method described in step S 106 . In addition, as a density correction amounts that are stored in the correction table, a correction amount for changing a pixel value in an image to be formed is stored. 
     Note that creation of a correction table and creation of a sinusoidal parameter, which have been described above, may be performed at a plurality of positions in the main scanning direction. 
       FIG.  10    illustrates combinations of a direction of density unevenness, the density of a correction target, a correction-amount storing method, and a correction method when density unevenness correction, which has been described above, is performed. 
     It is understood from each of the combinations illustrated in  FIG.  10    that a correction amount for correcting periodic density unevenness in the subscanning direction that is caused by a rotating body such as each of the photoconductor rollers  152  or each of the developing rollers  157  is stored as a sinusoidal parameter and that a correction amount for correcting density unevenness in the subscanning direction that is caused by a factor other than a rotating body is stored as a correction table. 
     Note that, although two methods, which are a method of changing light exposure and a method of changing a pixel value, are each provided as a method of correcting density unevenness, the method of changing a pixel value is not usable in the case of performing density correction of the solid density. This is because, in the case of trying to increase a pixel value in an image in order to correct density unevenness, it is impossible to set a gradation area percentage Cin to be greater than 100%, and thus, it is difficult to perform such correction by increasing density. In other words, in the case of performing density correction of the solid density, density correction is performed by changing light exposure. 
     Lastly, processing that is performed when an image is actually formed by using a correction amount for density correction calculated in the manner described above will be described with reference with the flowchart illustrated in  FIG.  11   . 
     First, in step S 201 , in response to input of image data for image formation, the density correction unit  21  determines a pixel to be processed. 
     Then, in step S 202 , the density correction unit  21  retrieves a correction amount for correcting the pixel value from a correction table stored in the correction table storing unit  22  on the basis of a position in the subscanning direction, a position in the main scanning direction, and a Z-phase signal of a rotating body and adds the correction amount to the pixel value of the pixel to be processed. 
     Next, in step S 203 , the density correction unit  21  calculates a correction amount that corresponds to the Z-phase signal of the rotating body on the basis of a sinusoidal parameter stored in the sinusoidal parameter storing unit  23 . Then, the density correction unit  21  adds the correction amount calculated on the basis of the sinusoidal parameter to the pixel value corrected by using the correction amount retrieved from the correction table. 
     Next, in step S 204 , the density correction unit  21  retrieves a correction amount for correcting light exposure from a correction table stored in the correction table storing unit  22  on the basis of the position of the pixel to be processed in the subscanning direction, the position of the pixel to be processed in the main scanning direction, and the Z-phase signal of the rotating body. 
     In addition, in step S 205 , the density correction unit  21  calculates a correction amount for correcting light exposure, the correction amount corresponding to the Z-phase signal of the rotating body, on the basis of a sinusoidal parameter stored in the sinusoidal parameter storing unit  23 . 
     Then, in step S 206 , the density correction unit  21  adds the correction amount for correcting light exposure, which has been retrieved from the correction table, and the correction amount for correcting light exposure, which has been calculated on the basis of the sinusoidal parameter. 
     Subsequently, in step S 207 , the density correction unit  21  corrects, by using the correction amount obtained by performing the above addition, the light exposure when the pixel to be processed is exposed to light by the exposure units  140 . 
     In the above-described density correction method for density unevenness in the subscanning direction, both density unevenness in the solid density and density unevenness in halftones are corrected by using a correction amount calculated on the basis of a sinusoidal parameter. The case where density unevenness in the solid density is corrected by using a correction amount based on a correction table will be described below. 
     The operation of the density correction unit  21  when density correction of periodic density unevenness in a solid density in the subscanning direction is performed by using a correction table will be described with reference with the flowchart illustrated in  FIG.  12   . 
     Note that the flowchart illustrated in  FIG.  12    is the same as the flowchart illustrated in  FIG.  6    except that step S 102  is replaced with step  102   a , and thus, only step S 102   a  will be described. 
     Also in the flowchart illustrated in  FIG.  12   , first, in step S 101 , the image output section forms a patch image having the solid density onto the intermediate transfer belt  16 , and the density correction unit  21  obtains a density variation profile that is continuous in the subscanning direction. In this case, the density variation profile is obtained such that a plurality of periods of a rotating body are included in the density variation profile. 
     Then, the density correction unit  21  creates, on the basis of the obtained density variation profile, a correction table that stores a correction amount for correcting density unevenness in the subscanning direction. 
     More specifically, the density correction unit  21  divides the density variation profile for each period of the rotating body by referencing to a Z-phase signal of the rotating body and averages the divided density variation profiles on the basis of their positions with respect to the Z phase. 
       FIG.  13    to  FIG.  15 B  illustrate the case of creating a correction table that stores a correction amount for correcting density unevenness that is caused by at least one of the photoconductor rollers  152 . 
       FIG.  13    illustrates an example of a density variation profile obtained by the density sensor  170 . The density variation profile illustrated in  FIG.  13    includes a plurality of periods T of at least one of the photoconductor rollers  152 . 
       FIG.  14    illustrates the state of the density variation profile illustrated in  FIG.  13    being divided by the period T of the photoconductor roller  152  and averaged. Referring to  FIG.  14   , it is understood that a single density variation profile is calculated by averaging the plurality of density variation profiles, which are obtained by dividing the density variation profile illustrated in  FIG.  13    by the period T of the photoconductor roller  152 . 
     After that, the density correction unit  21  creates a density correction profile that cancels out density variations caused by the photoconductor roller  152  by reversing the positive and negative components of the density variation profile obtained by the above averaging processing. 
       FIG.  15 A  and  FIG.  15 B  illustrate the case of determining a density correction amount by reversing the positive and negative components of the density variation profile.  FIG.  15 A  illustrates a density variation profile representing density variation amounts each corresponding to a rotation phase of one of the photoconductor rollers  152 , and  FIG.  15 B  illustrates a density correction amount profile in which density variations are canceled by reversing the positive and negative components in  FIG.  15 A . 
     Note that the density correction unit  21  performs the density correction by adjusting the light exposure of each of the exposure units  140 , and thus, the values stored in the actual correction table are multiplied by the sensitivity at the time of changing the light exposure. 
       FIG.  16    illustrates combinations of a direction of density unevenness, the density of a correction target, a correction-amount storing method, and a correction method when density unevenness correction, which has been described above, is performed. 
     It is understood from each of the combinations illustrated in  FIG.  16    that, among periodic density unevenness in the subscanning direction that is caused by a rotating body, such as each of the photoconductor rollers  152  or each of the developing rollers  157 , a correction amount for correcting density unevenness in the solid density is stored as a correction table, and a correction amount for correcting density unevenness in halftones is stored as a sinusoidal parameter. 
     As described above, only some of correction amounts for correcting periodic density unevenness in the subscanning direction that is caused by a rotating body may be stored as sinusoidal parameters, and the other correction amounts may be stored as correction tables. 
     Next, the case where a user or a person who is a customer engineer (CE) and who is in charge of maintenance is capable of switching a method of correcting density unevenness will be described. 
     In the following description, for example, the density correction unit  21  includes a first correction unit  51  and a second correction unit  52  as illustrated in  FIG.  17   . 
     Here, when a density variation profile that is density variation data obtained as a result of the density sensor  170  detecting the density of a patch image, which is a test image, is input, the first correction unit  51  creates, on the basis of the input density variation profile, a correction table that stores correction amounts for correcting periodic density unevenness due to a rotating body and density unevenness not due to a rotating body. 
     The second correction unit  52  creates, on the basis of the input density variation profile, a sinusoidal parameter representing a correction amount for correcting periodic density unevenness that is caused by a rotating body and a correction table storing a correction amount for correcting density variations not due to a rotating body. 
     The CPU  41  included in the controller  20  displays, for example, an operation screen such as that illustrated in  FIG.  18    on the UI device  45 , so that an operation screen that prompts a user as to whether the user selects a first density correction method that gives priority to reducing density unevenness in halftones or a second density correction method that gives priority to reducing density unevenness near the highest density is displayed. 
     In the case where the first density correction method is selected on the displayed operation screen, the density correction unit  21  inputs a density variation profile created by detecting a halftone patch image to the first correction unit  51  and stores the created correction table into the correction table storing unit  22 . Then, when an image is formed in the image output section, the density correction unit  21  retrieves, for pixels in the full range of shades, a correction amount corresponding the rotation phase of a rotating body in the image output section and a correction amount corresponding to a position in the subscanning direction from the correction table and performs correction of the density of an image that is formed onto a recording medium. 
       FIG.  19    illustrates the operation of the density correction unit  21  when the first density correction method that gives priority to reducing density unevenness in halftones is selected as described above. As seen by referring to  FIG.  19   , in the density correction unit  21 , only the first correction unit  51  performs processing for correcting density unevenness. 
     In the case where the second density correction method is selected on the displayed operation screen, the density correction unit  21  inputs a density variation profile created by detecting a patch image having a density near the highest density to the first correction unit  51 , stores the created correction table into the correction table storing unit  22 , inputs a density variation profile created by detecting a halftone patch image to the second correction unit  52 , and stores the created correction table and a sinusoidal set value into the correction table storing unit  22  and the sinusoidal parameter storing unit  23 , respectively. Then, when an image is formed in the image output section, if the pixel value of a pixel to be formed is near the solid density, the density correction unit  21  retrieves a correction amount corresponding the rotation phase of a rotating body in the image output section and a correction amount corresponding to a position in the subscanning direction from the correction table and performs correction of the density of an image that is formed onto a recording medium. In addition, if the pixel value of a pixel to be formed is in halftones, the density correction unit  21  calculates a correction amount corresponding the rotation phase of a rotating body in the image output section on the basis of a sinusoidal parameter, retrieves a correction amount corresponding to a position in the subscanning direction from the correction table, and performs correction of the density of an image that is formed onto a recording medium. 
       FIG.  20    illustrates the operation of the density correction unit  21  when the second density correction method that gives priority to reducing density unevenness near the solid density is selected as described above. As seen by referring to  FIG.  20   , in the density correction unit  21 , the first correction unit  51  corrects periodic density unevenness and nonperiodic density unevenness in the solid density by using a correction table, and in contrast, the second correction unit  52  corrects periodic density unevenness in a halftone density by using a sinusoidal parameter and corrects nonperiodic density unevenness by using a correction table. 
     In the embodiments above, the term “processor” refers to hardware in a broad sense. Examples of the processor include general processors (e.g., CPU: Central Processing Unit) and dedicated processors (e.g., GPU: Graphics Processing Unit, ASIC: Application Specific Integrated Circuit, FPGA: Field Programmable Gate Array, and programmable logic device). 
     In the embodiments above, the term “processor” is broad enough to encompass one processor or plural processors in collaboration which are located physically apart from each other but may work cooperatively. The order of operations of the processor is not limited to one described in the embodiments above, and may be changed. 
     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.