Patent Publication Number: US-11025799-B2

Title: Image forming apparatus correcting magnification of image in scanning direction of light beam

Description:
BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention relates to an image forming apparatus including a deflector configured to deflect a light beam. 
     Description of the Related Art 
     An electrophotographic image forming apparatus is configured to deflect a light beam emitted from a light source based on an image signal with a rotary polygon mirror, and cause the deflected light beam to form an image as a light spot scanned on a photosensitive member at a constant speed by an fθ lens. However, a scanning position of the light spot by the fθ lens may be positionally displaced by a part tolerance to distort an output image. To address this problem, in Japanese Patent Application Laid-Open No. 2009-17396, at a time when an image forming apparatus is assembled, a magnification of an image with respect to a scanning position is measured, a measurement result is stored in advance as a profile magnification, and an image signal is corrected based on the profile magnification. 
     Meanwhile, in an image forming apparatus configured to overlap a plurality of colors with one another to form a color image, a magnification of an image of each color may be changed by a part tolerance, a temperature in use, and a change with time to cause color misregistration among the images of the plurality of colors overlapped with one another. To address this problem, in Japanese Patent Application Laid-Open No. H07-52468, a color misregistration measurement pattern for measuring the color misregistration is formed, and a color misregistration magnification of an image of each color is corrected based on a detection result of the color misregistration measurement pattern. 
     However, when the magnification of the image with respect to the scanning position and the magnification for correcting the color misregistration are corrected in combination, a position at which the magnification of the image with respect to the scanning position is corrected may be displaced in accordance with the magnification for correcting the color misregistration. The displacement of the corrected position has a problem in that a density variation or moire is caused in the images of the plurality of colors overlapped with one another. 
     SUMMARY OF THE INVENTION 
     In view of the above-mentioned circumstances, the present invention provides an image forming apparatus capable of reducing color misregistration at a time when a first magnification and a second magnification of an image in a main scanning direction are corrected in combination. 
     According to one embodiment of the present invention, there is provided an image forming apparatus comprising: 
     a light source configured to emit a light beam based on an image signal; 
     a deflector configured to deflect the light beam so that the light beam emitted from the light source is scanned on a surface of a photosensitive member in a main scanning direction; 
     a storage portion configured to store a first magnification of an image with respect to a scanning position in the main scanning direction; and 
     a controller configured to generate a second magnification of the image with respect to a reference color image, 
     wherein the controller generates a third magnification based on the first magnification corrected based on the second magnification and the second magnification to correct the image signal based on the third magnification. 
     Further features of the present invention will become apparent from the following description of exemplary embodiments with reference to the attached drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a cross-sectional view of an image forming apparatus. 
         FIG. 2  is a plan view for schematically illustrating components that are arranged inside a light scanning apparatus. 
         FIG. 3  is a flowchart for illustrating magnification correction operation on an image in a main scanning direction. 
         FIG. 4A  and  FIG. 4B  are an explanatory view and an explanatory diagram of a profile measuring device, respectively. 
         FIG. 5  is a graph for showing a displacement amount with respect to a scanning position. 
         FIG. 6  is a graph for showing a profile magnification with respect to the scanning position. 
         FIG. 7  is a diagram for illustrating color misregistration measurement patterns and pattern detectors. 
         FIG. 8  is a graph for showing a displacement amount with respect to the scanning position. 
         FIG. 9  is a graph for showing a profile magnification and a composite magnification with respect to the scanning position. 
         FIG. 10  is an enlarged graph for showing an end of the profile magnification and the composite magnification with respect to the scanning position. 
         FIG. 11  is a graph for showing a profile magnification and a composite magnification with respect to the scanning position in a case of no fθ lens. 
         FIG. 12  is an enlarged graph of an end of the profile magnification and the composite magnification with respect to the scanning position in the case of no fθ lens. 
         FIG. 13  is a flowchart for illustrating magnification correction operation on an image in the main scanning direction in the case of no fθ lens. 
         FIG. 14  is a graph for showing a corrected displacement amount with respect to the scanning position. 
         FIG. 15  is a graph for showing a profile magnification and a corrected composite magnification with respect to the scanning position. 
         FIG. 16  is an enlarged graph of an end of the profile magnification and the corrected composite magnification with respect to the scanning position. 
         FIG. 17A ,  FIG. 17B , and  FIG. 17C  are diagrams for illustrating relationships between an output image and a corrected pixel position. 
         FIG. 18  is a flowchart for illustrating image forming control operation. 
         FIG. 19  is a block diagram of an image controller. 
         FIG. 20A ,  FIG. 20B , and  FIG. 20C  are diagrams for illustrating an image signal and a pixel size. 
         FIG. 21  is a diagram for illustrating magnifications and pixel sizes in continuous output operation of image signals. 
         FIG. 22  is a flowchart for illustrating image forming control operation based on displacement between corrected pixel positions. 
         FIG. 23  is a block diagram of an image controller based on displacement between corrected pixel positions. 
         FIG. 24  is a diagram for illustrating magnifications and pixel sizes in continuous output operation of image signals. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     Modes for carrying out the present invention are described below with reference to the accompanying drawings. 
     First Embodiment 
     (Image Forming Apparatus) 
       FIG. 1  is a cross-sectional view of an image forming apparatus  100 . The image forming apparatus  100  is an electrophotographic digital color printer that uses toners (developers) of a plurality of colors to form a color image on a recording medium (hereinafter referred to as “sheet”). The image forming apparatus  100  includes an image reading unit  700  configured to read an image of an original, and an image forming unit  701  configured to form the image on a sheet. 
     ((Image Reading Unit)) 
     The image reading unit  700  includes an original glass plate  702 , an illumination device  703 , reflecting mirrors  704   a ,  704   b , and  704   c , an imaging lens  705 , and an image sensor  706  (e.g., CCD) formed of a plurality of light receivers. The illumination device  703  illuminates the original placed on the original glass plate  702 . Light reflected by the original is reflected by the reflecting mirrors  704   a ,  704   b , and  704   c  to be guided to the imaging lens  705 . The imaging lens  705  images the reflected light on the image sensor  706 . The image sensor  706  is a photoelectric conversion element. The image sensor  706  separates colors of the reflected light from the original to convert image information of a blue component (B), image information of a green component (G), and image information of a red component (R) into electrical image data  30 . The image data  30  output from the image sensor  706  is input to an image controller  20  included in the image forming unit  701 . The image controller  20  serving as a controller includes a CPU  21 , a memory  22 , and a color conversion processing portion  23  ( FIG. 2 ). The color conversion processing portion  23  performs color conversion processing based on an intensity level of each of an image signal of the blue component (B), an image signal of the green component (G), and an image signal of the red component (R) of the image data  30 . The color conversion processing portion  23  generates a black (K) image signal  31 K, a cyan (C) image signal  31 C, a magenta (M) image signal  31 M, and a yellow (Y) image signal  31 Y. The image signals  31 K,  31 C,  31 M, and  31 Y are input to light scanning apparatus (laser scanner units)  707 K,  707 C,  707 M, and  707 Y, respectively. 
     ((Image Forming Unit)) 
     The image forming unit  701  includes four image forming portions  70  ( 70 Y,  70 M,  70 C, and  70 K). The image forming portion  70 Y forms a yellow image with the use of a yellow toner. The image forming portion  70 M forms a magenta image with the use of a magenta toner. The image forming portion  70 C forms a cyan image with the use of a cyan toner. The image forming portion  70 K forms a black image with the use of a black toner. The suffixes Y, M, C, and K in the reference symbols represent yellow, magenta, cyan, and black, respectively. In the following description, the suffixes Y, M, C, and K in the reference symbols may be omitted when the suffixes are not particularly necessary. The four image forming portions  70  have the same structure except for the color of the toner. 
     Each image forming portion  70  has a photosensitive drum (image bearing member)  708  serving as a photosensitive member. The photosensitive drum  708  rotates about a rotation axis  7  in a direction indicated by an arrow R 1  of  FIG. 1  when an image is formed. A charging device  709 , the light scanning apparatus  707 , a developing device  710 , a primary transfer device  712 , and a drum cleaning device (not shown) are arranged around the photosensitive drum  708 . An endless belt (hereinafter referred to as “intermediate transfer belt”)  711  serving as an intermediate transfer member is arranged below the photosensitive drum  708 . The intermediate transfer belt  711  is stretched over a drive roller  713 , a tension roller  715 , and a secondary transfer opposite roller  714 . The intermediate transfer belt  711  rotates in a direction indicated by an arrow R 2  of  FIG. 1  when an image is formed. On an upper surface of a horizontal portion of the intermediate transfer belt  711 , a photosensitive drum  708 Y, a photosensitive drum  708 M, a photosensitive drum  708 C, and a photosensitive drum  708 K are arranged in the stated order along a rotation direction R 2  of the intermediate transfer belt  711 . The primary transfer device  712  is opposed to the photosensitive drum  708  through the intermediate transfer belt  711 . A secondary transfer roller  716  is opposed to the secondary transfer opposite roller  714  through the intermediate transfer belt  711 . 
     A section that is downstream of the image forming portion  70  and that is near the intermediate transfer belt  711  is provided with pattern detectors (color misregistration measurement sensors)  726 , which are optical sensors configured to detect color misregistration measurement patterns (toner images) that are formed on the intermediate transfer belt  711 . The color misregistration measurement patterns are formed on the intermediate transfer belt  711  before an image is formed on the sheet or between formation of an image and formation of another image, and are detected by the pattern detectors  726 . Detection results of the pattern detectors  726  are used to correct a position and a magnification of an image. A section that is upstream of the image forming portion  70  and that is near the intermediate transfer belt  711  is provided with a belt cleaning device  717  configured to remove residual toner that remains on the intermediate transfer belt  711  after secondary transfer. 
     A feeding cassette  718  configured to contain sheets S is arranged in a lower part of the image forming apparatus  100 . The sheets S are fed from the feeding cassette  718  by a pickup roller  719 . The top sheet of the sheets fed by the pickup roller  719  is separated by a separation roller pair  722 , which is formed of a feed roller  722   a  serving as a conveying unit and a retard roller  722   b  serving as a separation unit. The sheet fed by the separation roller pair  722  is conveyed to a registration roller pair  723  by a plurality of conveying roller pairs  721  and  720 . A leading edge of the sheet is abutted against a nip of the registration roller pair  723  that has stopped rotating. When the sheet is formed into a loop, conveyance of the sheet is stopped once. The formation of the loop corrects skew feeding of the sheet. When the registration roller pair  723  starts rotating, the sheet is conveyed to the secondary transfer roller  716 . A fixing device  724  is arranged downstream of the secondary transfer roller  716  in a conveying direction of the sheet. A discharge tray  725 , on which the sheets with images formed thereon are stacked, is arranged downstream of the fixing device  724  in the conveying direction of the sheet. 
     (Image Forming Process) 
     An image forming process of the image forming apparatus  100  is described. The photosensitive drums  708 Y,  708 M,  708 C, and  708 K rotate in the direction indicated by the arrow R 1  about rotation axes  7 Y,  7 M,  7 C, and  7 K thereof, respectively. In the yellow image forming portion  70 Y, a charging device  709 Y charges a surface of the photosensitive drum  708 Y uniformly. The light scanning apparatus  707 Y emits laser light (hereinafter referred to as “light beam”) that is modulated based on the yellow component image signal  31 Y to form an electrostatic latent image on the uniformly charged surface of the photosensitive drum  708 Y. A developing device  710 Y develops the electrostatic latent image with the use of a yellow toner to obtain a yellow toner image. 
     Next, in the magenta image forming portion  70 M, a charging device  709 M charges a surface of the photosensitive drum  708 M uniformly. The magenta light scanning apparatus  707 M starts emitting a light beam that is modulated based on the magenta component image signal  31 M when a first predetermined time period passes after timing at which the yellow light scanning apparatus  707 Y starts writing the electrostatic latent image in a sub scanning direction. The light scanning apparatus  707 M scans the light beam on the uniformly charged surface of the photosensitive drum  708 M in a main scanning direction to form an electrostatic latent image. A developing device  710 M develops the electrostatic latent image with the use of a magenta toner to obtain a magenta toner image. 
     Next, in the cyan image forming portion  70 C, a charging device  709 C charges a surface of the photosensitive drum  708 C uniformly. The cyan light scanning apparatus  707 C starts emitting a light beam that is modulated based on the cyan component image signal  31 C when a second predetermined time period passes after timing at which the magenta light scanning apparatus  707 M starts writing the electrostatic latent image in the sub scanning direction. The light scanning apparatus  707 C scans the light beam on the uniformly charged surface of the photosensitive drum  708 C in the main scanning direction to form an electrostatic latent image. A developing device  710 C develops the electrostatic latent image with the use of a cyan toner to obtain a cyan toner image. 
     Next, in the black image forming portion  70 K, a charging device  709 K charges a surface of the photosensitive drum  708 K uniformly. The black light scanning apparatus  707 K starts emitting a light beam that is modulated based on the black component image signal  31 K when a third predetermined time period passes after timing at which the cyan light scanning apparatus  707 C starts writing the electrostatic latent image in the sub scanning direction. The light scanning apparatus  707 K scans the light beam on the uniformly charged surface of the photosensitive drum  708 K in the main scanning direction to form an electrostatic latent image. A developing device  710 K develops the electrostatic latent image with the use of a black toner to obtain a black toner image. In the first embodiment, the first predetermined time period, the second predetermined time period, and the third predetermined time period are the same, but may be set to different time periods depending on the structure and conditions of the image forming apparatus  100 . 
     The intermediate transfer belt  711  rotates in the direction indicated by the arrow R 2 . The yellow toner image on the photosensitive drum  708 Y is transferred onto the intermediate transfer belt  711  in a primary transfer portion between the photosensitive drum  708 Y and a primary transfer device  712 Y. Next, the magenta toner image on the photosensitive drum  708 M is transferred in an overlapping manner onto the yellow toner image on the intermediate transfer belt  711  in a primary transfer portion between the photosensitive drum  708 M and a primary transfer device  712 M. Next, the cyan toner image on the photosensitive drum  708 C is transferred in an overlapping manner onto the magenta toner image on the intermediate transfer belt  711  in a primary transfer portion between the photosensitive drum  708 C and a primary transfer device  712 C. Finally, the black toner image on the photosensitive drum  708 K is transferred in an overlapping manner onto the cyan toner image on the intermediate transfer belt  711  in a primary transfer portion between the photosensitive drum  708 K and a primary transfer device  712 K. In this manner, the toner images of the four colors: yellow, magenta, cyan, and black are transferred onto the intermediate transfer belt  711  while being overlapped with one another in the stated order. 
     The sheet fed from the feeding cassette  718  waits at the registration roller pair  723 . The registration roller pair  723  starts rotating at the right timing such that the toner images on the intermediate transfer belt  711  match a position of the sheet. The sheet is conveyed to a secondary transfer portion between the secondary transfer roller  716  and the secondary transfer opposite roller  714  by the registration roller pair  723 . The four-color toner images on the intermediate transfer belt  711  are transferred at once onto the sheet by the secondary transfer roller  716 . The sheet with the toner images transferred thereon is conveyed to the fixing device  724  serving as an image fixing unit. The fixing device  724  heats and pressurizes the sheet to fix the toner images to the sheet and form a full-color image on the sheet. The sheet with the image formed thereon is discharged onto the discharge tray  725 . 
     (Light Scanning Apparatus) 
     The light scanning apparatus  707  serving as light beam emitting devices is described next.  FIG. 2  is a plan view for schematically illustrating components that are arranged inside the light scanning apparatus  707 . The four light scanning apparatus  707 Y,  707 M,  707 C, and  707 K have the same structure. The light scanning apparatus  707  includes a semiconductor laser chip (hereinafter referred to as “light source”)  10 , a collimator lens  11 , a rotary polygon mirror  12 , a motor  17  configured to rotate the rotary polygon mirror  12 , an fθ lens  15 , and a reflecting mirror  16 . The light scanning apparatus  707  also includes a beam detector (hereinafter referred to as “BD”)  14 , and a photodiode (hereinafter referred to as “PD”)  13  serving as a light receiver. The light scanning apparatus  707  further includes a light source drive portion (laser driver)  18  configured to drive the light source  10 , and a motor drive portion  19  configured to drive the motor  17 . 
     The light source  10  is an edge emitting laser configured to emit light beams in two directions from half mirrors formed on both end surfaces, respectively. The light source  10  is configured to emit a light beam as front light toward the collimator lens  11 , and also emit a light beam as rear light toward the PD  13 . The front light is guided to the surface of the photosensitive drum  708  to form an electrostatic latent image on the surface of the photosensitive drum  708 . The rear light is emitted with a light intensity that is a predetermined ratio of a light intensity of the front light to enter the PD  13  serving as a detector configured to detect the light intensity. In automatic power control (hereinafter referred to as “APC”) of the light source  10 , when receiving the rear light, the PD  13  serving as a photoelectric conversion unit converts the rear light into an electrical signal. The PD  13  outputs the electrical signal as a detection signal (hereinafter referred to as “PD signal”)  32  to the light source drive portion  18 . The light source drive portion  18  adjusts the light intensity of the light beam emitted from the light source  10  based on the PD signal  32 . The light source  10  in the first embodiment is not limited to an edge emitting laser, but may be a surface emitting laser, for example, a vertical cavity surface emitting laser (VCSEL) or a vertical external cavity surface emitting laser (VECSEL). Moreover, the light source  10  may be a single beam generating unit configured to emit a single light beam, or a multi-beam generating unit configured to emit a plurality of light beams. 
     The light source  10  emits the light beam based on the image signal  31  of the corresponding color component. The collimator lens  11  converts the light beam emitted from the light source  10  into a substantially parallel light beam. The motor drive portion  19  outputs an acceleration/deceleration signal (hereinafter referred to as “drive signal”)  34  to the motor  17 , which is integrally formed with the rotary polygon mirror  12  serving as a deflector, to rotate the rotary polygon mirror  12  at a predetermined speed in a direction indicated by an arrow R 3  of  FIG. 2 . The light beam forms an image on a reflecting surface of the revolving rotary polygon mirror  12 , and is deflected by the rotary polygon mirror  12 . The light beam reflected by the rotary polygon mirror  12  passes through the fθ lens  15 , is reflected by the reflecting mirror  16 , and forms an image as a light spot that travels on the photosensitive drum  708  in the main scanning direction indicated by an arrow MS of  FIG. 2  at a constant speed. The fθ lens  15  converts the light beam that has been scanned at a constant angular velocity by the rotary polygon mirror  12  into the light spot that travels in the main scanning direction MS at the constant speed. 
     The light beam emitted from the light source  10  outside an image forming area is reflected by the rotary polygon mirror  12 , and enters the BD  14 . The BD  14  serving as a beam detector receives the light beam, and outputs a synchronization signal (hereinafter referred to as “BD signal”)  33  for making constant a writing start position of an electrostatic latent image on the photosensitive drum  708 , which is scanned with the light beam at a constant position in the main scanning direction. The BD signal  33  is input to the motor drive portion  19  and the image controller  20 . The motor drive portion  19  executes feedback control of a rotation speed of the motor  17  such that a period of the BD signal  33  is stabilized at a predetermined period. The image controller  20  outputs the image signal  31  to the light source drive portion  18  based on the BD signal  33 . After executing the APC, the light source drive portion  18  determines light beam emission start timing based on the BD signal  33 , and starts writing an image. In this manner, writing start positions in the main scanning direction of the image are matched. 
     The light source drive portion  18  outputs, to the light source  10 , a drive signal  35  for flashing the light source  10  based on the image signal  31  output from the image controller  20 . The light source drive portion  18  drives the light source  10  based on the image signal  31  at timing at which the light beam is scanned on an image forming area of the photosensitive drum  708 . The light source  10  emits the light beam modulated based on the image signal  31 . The light spot of the light beam emitted from the light source  10  and deflected by the rotary polygon mirror  12  travels on the surface of the photosensitive drums  708 , which is charged uniformly by the charging device  709 , in parallel to the rotation axis  7  of the photosensitive drum  708  in a linear pattern at a constant speed. An electric potential on the surface of the photosensitive drum  708  varies depending on the intensity of the light beam. The photosensitive drum  708  is repeatedly scanned with the light beam in the main scanning direction MS while being rotated in the sub-scanning direction R 1 , which is perpendicular to the main scanning direction MS, with the result that the electrostatic latent image is formed in the sub-scanning direction R 1 . 
     (Magnification Correction of Image) 
     However, depending on an individual difference of the fθ lens  15 , a temperature change, or a change with time, the images of the respective colors may not be overlapped with one another correctly in the main scanning direction MS to cause color misregistration in some cases. In order to avoid the color misregistration, a magnification in the main scanning direction MS of an image is corrected. Now, referring to  FIG. 3 , magnification correction on an image in the main scanning direction MS is described.  FIG. 3  is a flowchart for illustrating magnification correction operation on an image in the main scanning direction MS. 
     ((Profile Magnification Correction)) 
     First, in order to correct color misregistration caused by a component that cannot be completely corrected by the fθ lens  15  or an individual difference at the time of production, the light beam of the light scanning apparatus  707  is measured in advance by a profile measuring device  40 , and a measurement result is stored in the memory  22 . At the time of image formation, the measurement result is read from the memory  22 , and the image data is corrected based on a magnification of a profile determined based on the measurement result. The profile is magnification property information indicating a magnification with respect to a position (hereinafter referred to as “scanning position”) X in the main scanning direction MS for each light scanning apparatus  707 . A correction amount for correcting the magnification of the profile is hereinafter referred to as “profile magnification (first magnification) Mag_P”. Correction of the image data based on the profile magnification Mag_P is referred to as “profile magnification correction”. The profile magnification correction allows the light spot that forms an image on the photosensitive drum  708  to travel at the constant speed. A measurement operation using the profile measuring device  40  is performed before the light scanning apparatus  707  is assembled into the image forming apparatus  100 . 
       FIG. 4A  and  FIG. 4B  are an explanatory view and an explanatory diagram of the profile measuring device  40 , respectively.  FIG. 4A  is a perspective view of the profile measuring device  40 . The profile measuring device  40  includes a front detector  41 , a center detector  42 , and a rear detector  43 , which are arrayed in line in the main scanning direction MS.  FIG. 4B  is a diagram for illustrating a positional relationship among the BD  14 , which is provided in the light scanning apparatus  707 , and the front detector  41 , the center detector  42 , and the rear detector  43 , which are provided in the profile measuring device  40 . From upstream to downstream in the main scanning direction MS, the BD  14 , the front detector  41 , the center detector  42 , and the rear detector  43  are arranged in the stated order at the same interval Sx. In the first embodiment, the interval (inter-detector distance) Sx is set to 100 mm, but the present invention is not limited thereto. 
     When the light beam emitted from the light scanning apparatus  707  passes above the front detector  41 , the center detector  42 , and the rear detector  43 , each of the front detector  41 , the center detector  42 , and the rear detector  43  outputs an electrical signal. Times Tf, Tc, and Tr at which the light beam passes above the front detector  41 , the center detector  42 , and the rear detector  43 , respectively, are measured with reference to the BD signal  33  output from the BD  14 . The time Tf is the time it takes for the light beam to travel from the BD  14  to the front detector  41 . The time Tc is the time it takes for the light beam to travel from the BD  14  to the center detector  42 . The time Tr is the time it takes for the light beam to travel from the BD  14  to the rear detector  43 . Displacement amounts ΔSf, ΔSc, and ΔSr of the light beam with respect to the scanning position X in the main scanning direction MS are determined based on the times Tf, Tc, and Tr. The scanning position X has its origin (X=0) at the position of the center detector  42 . The scanning position X of the front detector  41  is −Sx (X=−Sx). The scanning position X of the rear detector  43  is Sx (X=Sx). The displacement amount ΔSf indicates a displacement amount from an ideal scanning position at a time when the light beam is at the scanning position X=−Sx. The displacement amount ΔSc indicates a displacement amount from an ideal scanning position at a time when the light beam is at the scanning position X=0. The displacement amount ΔSr indicates a displacement amount from an ideal scanning position at a time when the light beam is at the scanning position X=Sx. When a light beam scanning speed is represented by V, the displacement amounts ΔSf, ΔSc, and ΔSr are expressed by the following expressions.
 
Δ Sf=Sx −( Tf×V )
 
Δ Sc =(2 ×Sx )−( Tc×V )
 
Δ Sr =(3× Sx )−( Tr×V )
 
     For example, when the scanning speed V is 1 mm/μs, the interval (inter-detector distance) Sx is 100 mm, and the time Tf at which the light beam passes above the front detector  41  is 101 μs, the displacement amount ΔSf is −1 mm. 
     The measured values of the displacement amounts ΔSf, ΔSc, and ΔSr are stored in the memory (storage portion)  22  of the image controller  20 . The values of the displacement amounts ΔSf, ΔSc, and ΔSr are used in correcting the magnification of a pixel in the main scanning direction MS based on the profile during the image formation (hereinafter referred to as “profile magnification correction”). When image forming operation is started, the CPU  21  starts the magnification correction operation in accordance with the flowchart of  FIG. 3 . The CPU  21  reads the values of the displacement amounts ΔSf, ΔSc, and ΔSr from the memory  22 . The CPU  21  calculates a displacement amount Y with respect to the scanning position X based on the values of the displacement amounts ΔSf, ΔSc, and ΔSr.  FIG. 5  is a graph for showing the displacement amount Y with respect to the scanning position X. When measurement results of the three detectors: the front detector  41 , the center detector  42 , and the rear detector  43  are used, an approximation of the displacement amount Y with respect to the scanning position X is expressed as a quadratic. The displacement amount Y with respect to the scanning position X is expressed by Expression 1 below. 
     
       
         
           
             
               
                 
                   Y 
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                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             Sr 
                           
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                             Δ 
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                             ⁢ 
                             Sf 
                           
                           - 
                           
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                             Sr 
                           
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                       Sc 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Expression 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
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     In the first embodiment, a scanning area in the main scanning direction MS is divided into eight areas (hereinafter referred to as “blocks”) (Block  1  to Block  8 ). A displacement amount Mag_Block(N) is set for each block. In the first embodiment, Block  1  to Block  8  are set to have the same width, and Block  1  to Block  8  are arranged at equal intervals. However, the width (interval) of the block may be set smaller toward ends with a larger variation in displacement amount. The displacement amount Mag_Block(N) of each block is expressed by Expression 2 below. 
     
       
         
           
             
               
                 
                   
                     Mag_Block 
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                       ( 
                       N 
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                           ( 
                           
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                       Block_Width 
                       ⁢ 
                       
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                   ) 
                 
               
             
           
         
       
     
     In Expression 2, N represents a block number, and n represents a coordinate at the left end of Block N. Y(n) represents a displacement amount at the left end of Block N, and Y(n+1) represents a displacement amount at the left end of Block N+1. Block_Width(N) represents a width of Block N. 
     For example, when the measurement results of the displacement amounts are ΔSf=−0.32 mm, ΔSc=0 mm, and ΔSr=−0.32 mm, and a scanning area of 320 mm is divided into eight blocks, the profile magnification Mag_P as shown in  FIG. 6  is obtained.  FIG. 6  is a graph for showing the profile magnification Mag_P (%) with respect to the scanning position X mm. The CPU  21  calculates the profile magnification Mag_P based on the values of the displacement amounts ΔSf, ΔSc, and ΔSr stored in the memory  22  (Step S 1 ). In the first embodiment, the profile magnification Mag_P is set for each block based on the displacement amount Mag_Block(N) of each block. The CPU  21  starts the profile magnification correction for correcting the image data based on the profile magnification set for each block (Step S 2 ). Through the correction of the image data at each scanning position X based on the profile magnification Mag_P set for each block, the color misregistration caused by the component that cannot be completely corrected by the fθ lens  15  or an individual difference at the time of production can be corrected. When a calculation speed of the CPU  21  with respect to a printing speed is sufficiently fast, the profile magnification Mag_P may be set for each pixel based on Expression 1. The CPU  21  executes the calculation of the profile magnification Mag_P and the profile magnification correction, which have been described above, for the light scanning apparatus  707  of each color. 
     ((Color Misregistration Magnification Correction)) 
     In order to correct a magnification that varies depending on the temperature, the change with time, and other such factors, the CPU  21  corrects the image data. A correction amount for correcting the magnification that varies depending on the temperature, the change with time, and other such factors are hereinafter referred to as “color misregistration magnification (second magnification) Mag_I”. The correction of the image data based on the color misregistration magnification Mag_I is referred to as “color misregistration magnification correction”. In the color misregistration magnification correction, the color misregistration measurement patterns are formed on the intermediate transfer belt  711  with the use of the image data that has been subjected to the profile magnification correction. The CPU  21  detects the color misregistration measurement patterns with the pattern detectors  726  (Step S 3 ).  FIG. 7  is a diagram for illustrating color misregistration measurement patterns  727  and  728  and pattern detectors  726   a  and  726   b . Color misregistration magnification correction of a target color image corrects the displacement amount with respect to a reference color image. Yellow is hereinafter referred to as “reference color”, and colors (magenta, cyan, and black) other than the reference color are hereinafter referred to as “target colors”. In steps similar to those in the case where the toner images are transferred to the sheet, the color misregistration measurement patterns as the toner images are formed on the intermediate transfer belt  711  by the primary transfer device  712 , and the color misregistration measurement patterns are detected by the pattern detectors  726  provided at an end of the intermediate transfer belt  711 . As illustrated in  FIG. 7 , the pattern detectors  726  include a front pattern detector  726   a  on an upstream side (hereinafter referred to as “front side”) in the main scanning direction MS, and a rear pattern detector  726   b  on a downstream side (hereinafter referred to as “rear side”) in the main scanning direction MS. At each of positions on the intermediate transfer belt  711  that pass below the front pattern detector  726   a  and the rear pattern detector  726   b , the color misregistration measurement patterns  727  and  728 , which are the same patterns, are formed. The color misregistration measurement patterns  727  on the front side include reference color patterns (first patterns)  727   a  and  727   c  having oblique line shapes, and target color patterns (second patterns)  727   b  and  727   d  having oblique line shapes. Similarly, the color misregistration measurement patterns  728  on the rear side include reference color patterns (first patterns)  728   a  and  728   c  having oblique line shapes, and target color patterns (second patterns)  728   b  and  728   d  having oblique line shapes. An interval between the reference color patterns  727   a  and  727   c  ( 728   a  and  728   c ), and an interval between the target color patterns  727   b  and  727   d  ( 728   b  and  728   d ) are measured to measure the displacement amount in the main scanning direction MS of an image of a target color with respect to an image of the reference color. 
     Now, there is described measurement of the displacement amount (positional displacement amount) in the main scanning direction MS of an image of magenta as a target color with respect to an image of yellow as the reference color. The front pattern detector  726   a  detects an interval Ref(F) between yellow reference color patterns  727   a  and  727   c  and an interval Tar(F) between magenta target color patterns  727   b  and  727   d . Similarly, the rear pattern detector  726   b  detects an interval Ref(R) between yellow reference color patterns  728   a  and  728   c  and an interval Tar(R) between magenta (M) target color patterns  728   b  and  728   c.    
     The displacement amount ΔRf of magenta with respect to yellow on the front side is expressed as follows.
 
Δ Rf =( Tar ( F )−Ref( F ))/2
 
     The displacement amount ΔRr of magenta with respect to yellow on the rear side is expressed as follows.
 
Δ Rr =( Tar ( R )−Ref( R ))/2
 
     The scanning position X at which the front pattern detector  726   a  is arranged is represented by −Rx, and the scanning position X at which the rear pattern detector  726   b  is arranged is represented by +Rx.  FIG. 8  is a graph for showing the displacement amount with respect to the scanning position X. The number of points of measurement of the displacement amount is two, and hence the displacement amount Y in the main scanning direction MS of the target color with respect to the reference color is expressed as the following approximation of a linear function as shown in  FIG. 8 . 
     
       
         
           
             Y 
             = 
             
               
                 
                   
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       Rr 
                     
                     - 
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       Rf 
                     
                   
                   
                     2 
                     × 
                     
                       R 
                       x 
                     
                   
                 
                 ⁢ 
                 x 
               
               + 
               
                 
                   
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Rr 
                   
                   + 
                   
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Rf 
                   
                 
                 2 
               
             
           
         
       
     
     In accordance with the approximation of the linear function above, a rate of change of the displacement amount Y is constant in all areas of the scanning position X in the main scanning direction MS. A Δ displacement amount, which is a difference between the displacement amount ΔRf on the front side and the displacement amount ΔRr on the rear side in the main scanning direction MS, is obtained from an interval (2×Rx) between the front pattern detector  726   a  and the rear pattern detector  726   b  by the following expression. 
     
       
         
           
             
               Δ 
               ⁢ 
               
                   
               
               ⁢ 
               Displacement 
               ⁢ 
               
                   
               
               ⁢ 
               Amount 
             
             = 
             
               
                 
                   
                     
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         Rr 
                       
                       - 
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         Rf 
                       
                     
                     
                       2 
                       × 
                       
                         R 
                         x 
                       
                     
                   
                   ⁢ 
                   
                     ( 
                     
                       - 
                       
                         R 
                         x 
                       
                     
                     ) 
                   
                 
                 + 
                 
                   
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       Rr 
                     
                     - 
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       Rf 
                     
                   
                   2 
                 
                 - 
                 
                   ( 
                   
                     
                       
                         
                           
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             Rr 
                           
                           - 
                           
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             Rf 
                           
                         
                         
                           2 
                           × 
                           
                             R 
                             x 
                           
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           + 
                           
                             R 
                             x 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           Rr 
                         
                         + 
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           Rf 
                         
                       
                       2 
                     
                   
                   ) 
                 
               
               = 
               
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   Rf 
                 
                 - 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   Rr 
                 
               
             
           
         
       
     
     The CPU  21  calculates the color misregistration magnification Mag_I based on the displacement amount ΔRf and the displacement amount ΔRr (Step S 4 ). The color misregistration magnification Mag_I (%) is expressed as Expression 3 below. 
     
       
         
           
             
               
                 
                   Mag_I 
                   = 
                   
                     
                       
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           Rf 
                         
                         - 
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           Rr 
                         
                       
                       
                         2 
                         × 
                         
                           R 
                           x 
                         
                       
                     
                     × 
                     100 
                   
                 
               
               
                 
                   ( 
                   
                     Expression 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                   ) 
                 
               
             
           
         
       
     
     For example, it is assumed that Rx=100 mm, that the interval between the front pattern detector  726   a  and the rear pattern detector  726   b  is 200 mm (2×Rx=200 mm), that ΔRf=2 mm, and that ΔRr=−2 mm. Based on Expression 3, the color misregistration magnification Mag_I is 2%. The detection and the calculation of the color misregistration measurement patterns  727  and  728  are performed also for remaining cyan and black to determine the color misregistration magnification Mag_I for each color. Color misregistration magnification correction for yellow, which is the reference color, is not performed, and color misregistration magnification correction is performed so as to match colors other than yellow to the reference color. In this manner, the CPU  21  serving as a color misregistration magnification generating portion generates the color misregistration magnification (second magnification) Mag_I of the target color image with respect to the reference color image based on detection results of the color misregistration measurement patterns  727  and  728 . 
     ((Composite Magnification Correction)) 
     The CPU  21  composites the profile magnification Mag_P and the color misregistration magnification Mag_I, which have been determined as described above, to calculate a composite magnification (third magnification) Mag with respect to each scanning position X (Step S 5 ). The composite magnification Mag is expressed as Expression 4 below. 
     
       
         
           
             
               
                 
                   Mag 
                   = 
                   
                     
                       ( 
                       
                         
                           
                             ( 
                             
                               1 
                               + 
                               
                                 Mag_P 
                                 100 
                               
                             
                             ) 
                           
                           ⁢ 
                           
                             ( 
                             
                               1 
                               + 
                               
                                 Mag_I 
                                 100 
                               
                             
                             ) 
                           
                         
                         - 
                         1 
                       
                       ) 
                     
                     × 
                     100 
                   
                 
               
               
                 
                   ( 
                   
                     Expression 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                   ) 
                 
               
             
           
         
       
     
     The image data is corrected based on the composite magnification Mag, which is determined as described above (Step S 6 ). The image is formed on the sheet based on the corrected image data (Step S 7 ). An image with reduced color misregistration can be formed by correcting the image data based on the composite magnification Mag. 
       FIG. 9  is a graph for showing the profile magnification Mag_P and the composite magnification Mag with respect to the scanning position X. The composite magnification Mag is generated by compositing the color misregistration magnification Mag_I of +2% with the profile magnification Mag_P. Along with enlargement in the main scanning direction MS of the image, which is caused by the correction of the image data based on the color misregistration magnification Mag_I, a corrected pixel position (first pixel position) based on the composite magnification Mag is displaced in the main scanning direction MS with respect to a corrected position of the image data based on the profile magnification Mag_P. FIG. is an enlarged graph of an end of the profile magnification Mag_P and the composite magnification Mag with respect to the scanning position X. As shown in  FIG. 10 , the displacement in the main scanning direction MS of the corrected pixel position (first pixel position) of the composite magnification Mag with respect to a corrected pixel position (second pixel position) of the profile magnification Mag_P is small, and hence does not pose a problem. 
     (Magnification Correction in Light Scanning Apparatus without fθ Lens) 
     In recent years, however, in order to reduce cost, the fθ lens  15  is omitted from the light scanning apparatus  707 . The fθ lens  15  has a function of converting the light beam that rotates at the constant angular velocity into the light spot that travels on the photosensitive drum  708  at the constant speed. In the light scanning apparatus  707  without the fθ lens  15 , image displacement is corrected through the profile magnification correction, and hence the profile magnification (correction amount) becomes larger as compared to the case of the light scanning apparatus  707  with the fθ lens  15 . When the profile magnification (correction amount) is increased, displacement of a pixel position in the profile magnification correction poses a problem.  FIG. 11  is a graph for showing a profile magnification Mag_P and a composite magnification Mag with respect to the scanning position X in a case of no fθ lens  15 .  FIG. 12  is an enlarged graph of an end of the profile magnification Mag_P and the composite magnification Mag with respect to the scanning position X in the case of no fθ lens  15 . As shown in  FIG. 11 , the profile magnification Mag_P of the image forming apparatus  100  without the fθ lens  15  is significantly increased as compared to the profile magnification Mag_P of the image forming apparatus  100  with the fθ lens  15 , which is shown in  FIG. 9 . Displacement in the main scanning direction MS of the corrected pixel position (first pixel position) of the composite magnification Mag with respect to the corrected pixel position (second pixel position) of the profile magnification Mag_P, which is shown in  FIG. 12 , is large as compared to the displacement in the case of the image forming apparatus  100  with the fθ lens  15 , which is shown in  FIG. 10 . Due to the displacement of the corrected pixel position, the color misregistration cannot be corrected sufficiently in some cases. 
     To address this problem, in the first embodiment, before the profile magnification Mag_P and the color misregistration magnification Mag_I are composited to generate the composite magnification Mag, the profile magnification Mag_P is corrected based on the color misregistration magnification Mag_I. As a result, even when the profile magnification Mag_P is large, the color misregistration of an image can be reduced. 
     ((Correction of Profile Magnification Based on Color Misregistration Magnification)) 
       FIG. 13  is a flowchart for illustrating magnification correction operation on an image in the main scanning direction MS in the case of no fθ lens  15 . Steps S 1  to S 4  of  FIG. 13  are the same as Steps S 1  to S 4  of  FIG. 3 , and hence descriptions thereof are omitted. Based on the color misregistration magnification Mag_I determined based on Expression 3, the displacement amount Y caused by the profile magnification determined based on Expression 1 is corrected (Step S 11 ). The CPU  21  calculates the displacement amount Y with respect to the scanning position X based on the values of the displacement amounts ΔSf, ΔSc, and ΔSr and the color misregistration magnification Mag_I. The displacement amount Y with respect to the scanning position X is expressed by Expression 5 below. 
     
       
         
           
             
               
                 
                   Y 
                   = 
                   
                     
                       
                         
                           
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             Sr 
                           
                           + 
                           
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             Sf 
                           
                           - 
                           
                             2 
                             ⁢ 
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             Sc 
                           
                         
                         
                           2 
                           × 
                           
                             S 
                             x 
                             2 
                           
                         
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             x 
                             × 
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                   Mag_I 
                                   100 
                                 
                               
                               ) 
                             
                           
                           ) 
                         
                         2 
                       
                     
                     + 
                     
                       
                         
                           
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             Sr 
                           
                           - 
                           
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             Sf 
                           
                         
                         
                           2 
                           × 
                           
                             S 
                             x 
                           
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           x 
                           + 
                           
                             ( 
                             
                               1 
                               + 
                               
                                 Mag_I 
                                 100 
                               
                             
                             ) 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       Sc 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Expression 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     5 
                   
                   ) 
                 
               
             
           
         
       
     
       FIG. 14  is a graph for showing the corrected displacement amount Y with respect to the scanning position X. As shown in  FIG. 14 , the scanning position X is corrected based on the color misregistration magnification Mag_I. The displacement amount Mag_Block(N) of each block is determined by substituting the displacement amount Y determined based on Expression 5 into Expression 2. The CPU  21  sets the profile magnification Mag_P for each block based on the displacement amount Mag_Block(N) of each block. In this manner, the CPU  21  corrects the profile magnification Mag_P based on the color misregistration magnification (Step S 12 ). 
     In the first embodiment, Expression 1 is modified with the color misregistration magnification Mag_I to obtain Expression 5. However, Expression 2 may be modified with the color misregistration magnification Mag_I to obtain the following expression for determining the displacement amount Mag_Block(N) of each block. 
     
       
         
           
             
               Mag_Block 
               ⁢ 
               
                 ( 
                 N 
                 ) 
               
             
             = 
             
               
                 
                   Y 
                   ⁡ 
                   
                     ( 
                     n 
                     ) 
                   
                 
                 - 
                 
                   Y 
                   ⁡ 
                   
                     ( 
                     
                       n 
                       + 
                       1 
                     
                     ) 
                   
                 
               
               
                 Block_Width 
                 ⁢ 
                 
                   
                     ( 
                     N 
                     ) 
                   
                   ÷ 
                   
                     ( 
                     
                       1 
                       + 
                       
                         Mag_I 
                         100 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
     The CPU  21  may set the profile magnification Mag_P for each block based on the displacement amount Mag_Block(N) of each block that is corrected based on the color misregistration magnification Mag_I. Also in this manner, the CPU  21  can correct the profile magnification Mag_P based on the color misregistration magnification. 
     The CPU  21  calculates the composite magnification Mag of the profile magnification Mag_P corrected based on the color misregistration magnification Mag_I and the color misregistration magnification Mag_I based on Expression 4 (Step S 13 ).  FIG. 15  is a graph for showing the profile magnification Mag_P and the corrected composite magnification Mag with respect to the scanning position X.  FIG. 16  is an enlarged graph of an end of the profile magnification Mag_P and the corrected composite magnification Mag with respect to the scanning position X. The corrected composite magnification Mag shown in  FIG. 15  and  FIG. 16  is generated by compositing the profile magnification Mag_P corrected based on the color misregistration magnification Mag_I and the color misregistration magnification Mag_I. The corrected composite magnification Mag has a smaller error from an ideal magnification as compared to the composite magnification Mag shown in  FIG. 12 , and hence the color misregistration of the color image formed on the sheet can be reduced. 
       FIG. 17A  and  FIG. 17B  are diagrams for illustrating relationships between an output image and the corrected pixel position.  FIG. 17A  is a diagram for illustrating a relationship between the output image that has been subjected to the profile magnification correction without the color misregistration magnification correction and the corrected pixel position.  FIG. 17B  is a diagram for illustrating a relationship between the output image that has been subjected to composite magnification correction of the profile magnification correction and the color misregistration magnification correction and the corrected pixel position. When the composite magnification correction is executed, as illustrated in  FIG. 17B , the output image and the corrected pixel position in the profile magnification correction are both scaled with the color misregistration magnification in the main scanning direction MS.  FIG. 17C  is a diagram for illustrating a relationship between the output image that has been subjected to the composite magnification correction of the profile magnification correction corrected by the color misregistration magnification correction and the color misregistration magnification correction and the corrected pixel position. When the composite magnification correction corrected by the color misregistration magnification correction is executed, as illustrated in  FIG. 17C , the output image is scaled, but the corrected pixel position in the profile magnification correction is unchanged. Therefore, through the execution of the corrected composite magnification correction, the image can be corrected at an appropriate magnification, and the color misregistration can be reduced. 
     The CPU  21  corrects the image data based on the corrected composite magnification Mag (Step S 14 ). The image is formed on the sheet based on the corrected image data (Step S 15 ). Through the correction of the image data based on the composite magnification Mag of the profile magnification correction corrected by the color misregistration magnification correction and the color misregistration magnification correction, the image with the reduced color misregistration can be formed. 
     According to the first embodiment, there can be reduced the color misregistration in the case where the profile magnification (first magnification) and the color misregistration magnification (second magnification) of the image in the main scanning direction are corrected in combination. 
     Second Embodiment 
     Now, a second embodiment of the present invention is described. In the second embodiment, structures similar to those in the first embodiment are denoted by similar reference symbols, and descriptions thereof are omitted. The image forming apparatus  100 , the image forming process, and the light scanning apparatus  707  in the second embodiment are similar to those in the first embodiment, and hence descriptions thereof are omitted. In the second embodiment, the composite magnification correction by the image controller  20  is described. The calculation of the profile magnification, the color misregistration magnification, and the composite magnification is similar to that in the first embodiment, and hence a description thereof is omitted. 
       FIG. 18  is a flowchart for illustrating image forming control operation.  FIG. 19  is a block diagram of the image controller  20 . The image controller  20  includes a CPU  21 , a memory  22 , an image data holding portion  24 , a profile magnification holding portion  25 , a color misregistration magnification holding portion  26 , a pixel size calculating portion  27 , a magnification compositing portion  28 , and an image signal output portion  29 . The CPU executes image forming operation as programmed by a program that is stored in the memory  22 . When the image forming control operation is started, the CPU  21  stores, in the image data holding portion  24 , the image data  30  output from the image reading unit  700 . The CPU  21  stores, in the profile magnification holding portion  25 , the profile magnification with respect to the scanning position X, which has been obtained based on the measurement result of the profile measuring device  40 . The CPU  21  stores, in the color misregistration magnification holding portion  26 , the color misregistration magnification obtained from the detection result of the pattern detectors  726 . 
     The CPU  21  determines whether a TOP signal  36  has been input to the pixel size calculating portion  27  (Step S 21 ). The TOP signal  36  is a synchronization signal of the light beam in the sub scanning direction R 1 . The TOP signal is used to print the top (first line) of an image at an appropriate position of the sheet. When the TOP signal has been input (YES in Step S 21 ), the CPU  21  determines whether a BD signal  33  has been input to the pixel size calculating portion  27  (Step S 22 ). When the light beam deflected by the rotary polygon mirror  12  enters the BD  14 , the BD  14  outputs the BD signal  33  to the pixel size calculating portion  27 . When the BD signal  33  has been input (YES in Step S 22 ), the pixel size calculating portion  27  starts processing on the first pixel of the first line with reference to the BD signal  33 . First, the pixel size calculating portion  27  reads the profile magnification of the first pixel from the profile magnification holding portion  25  (Step S 23 ). Next, the pixel size calculating portion  27  reads the color misregistration magnification from the color misregistration magnification holding portion  26  (Step S 24 ). The pixel size calculating portion uses the magnification compositing portion  28  to calculate the composite magnification of the profile magnification and the color misregistration magnification with the use of Expression 4 (Step S 25 ). 
     The pixel size calculating portion  27  calculates a pixel size based on the image data, the composite magnification, and an error amount at the time when the previous one pixel size is determined (Step S 26 ). In other words, the pixel size calculating portion  27  determines to what size one pixel is enlarged, reduced, or maintained in terms of the magnification. The pixel size calculating portion  27  outputs the calculated pixel size to the image signal output portion  29 . The image signal output portion  29  outputs, to the light source drive portion  18 , the image signal  31  corresponding to one pixel based on the calculated pixel size and the image data in the image data holding portion  24  (Step S 27 ). The light source drive portion  18  generates the drive signal  35  based on the image signal  31 , and outputs the drive signal  35  to the light source  10 . The light source  10  emits the light beam based on the drive signal  35  to form a latent image corresponding to one pixel on the photosensitive drum  708 . The CPU  21  determines whether output of image signals  31  corresponding to one line has been completed (Step S 28 ). When the output of the image signals  31  corresponding to one line has not been completed (NO in Step S 28 ), the processing returns to Step S 23 . The CPU  21  similarly corrects a pixel size of the next pixel. When the output of the image signals  31  corresponding to one line has been completed (YES in Step S 28 ), the CPU  21  determines whether the image formation has been completed (Step S 29 ). When the image formation has not been completed (NO in Step S 29 ), the processing returns to Step S 22 , and image signals  31  for the next line are generated. When the image formation has been completed (YES in Step S 29 ), the CPU  21  ends the image formation. 
     The determination of the size of one pixel and the output of the image signal  31  are described with reference to  FIG. 20A ,  FIG. 20B , and  FIG. 20C .  FIG. 20A ,  FIG. 20B , and  FIG. 20C  are diagrams for illustrating the image signal  31  and the pixel size. The image data  30  is generated as a bit data group obtained by being divided by a predetermined integer value for each pixel. One pixel is formed of a predetermined integer number of bit data (tiny pixel pieces). Inserting (add) at least one bit data into a bit data group of one pixel, and extracting (deleting) at least one bit data from the bit data group of one pixel are referred to as “bit data insertion/extraction”. The pixel size is a size (length) of one pixel in the main scanning direction MS. The size of one pixel in the main scanning direction MS is changed by the bit data insertion/extraction. When the size of one pixel is enlarged in the main scanning direction MS, at least one bit data is inserted into the bit data group of one pixel to increase the size of one pixel. When the size of one pixel is reduced in the main scanning direction MS, at least one bit data is extracted from the bit data group of one pixel to reduce the size of one pixel. In this manner, the magnification of the image in the main scanning direction MS can be changed by the bit data insertion/extraction. 
     For example, when the predetermined integer value is 100, one pixel of the image data  30  is formed of 100 bit data. When the magnification correction is not required, one pixel is formed of 100 bit data as illustrated in  FIG. 20A . When the image is enlarged by +30% magnification correction, 30 bit data is added to the original one pixel, with the result that the corrected one pixel is formed of 130 bit data as illustrated in  FIG. 20B . When the light beam is emitted from the light source  10  based on the image signal  31  formed of 130 bit data per pixel, an enlarged latent image is formed on the photosensitive drum  708 . ON the contrary, when the image is reduced by −30% magnification correction, 30 bit data is deleted from the original one pixel, with the result that the corrected one pixel is formed of 70 bit data as illustrated in  FIG. 20C . When the light beam is emitted from the light source  10  based on the image signal  31  formed of 70 bit data per pixel, a reduced latent image is formed on the photosensitive drum  708 . 
       FIG. 21  is a diagram for illustrating magnifications and pixel sizes in continuous output operation of image signals  31 . A pixel size of one pixel without magnification correction is 100 bit data. The color misregistration magnification is +2%. The profile magnification is −25% for the first Block  0 , and −20% for the next Block  1 . The pixel size of the first pixel is changed, based on the composite magnification of −23.5% that has been calculated by the magnification compositing portion  28 , from 100 bit data to 77 bit data by the pixel size calculating portion  27 . The pixel size is 76.5 bit data in calculation, but is determined as 77 bit data because the image signal  31  is output in units of 1 bit data. Therefore, an error of −0.5 bit data is generated. The error of −0.5 bit data is used when a pixel size of the next pixel is determined. The next one pixel is also 76.5 bit data in calculation, but is output as 76 bit data based on the error of −0.5 bit data. Such calculation of the pixel size is repeated such that the image as a whole is scaled to a target magnification. Further, at around the center of  FIG. 21 , the block of the profile magnification, which has been described in the first embodiment, is switched from Block  0  to Block  1 . When the block has been switched from Block  0  to Block  1 , the profile magnification of −20% of Block  1  is read from the profile magnification holding portion  25 . The magnification compositing portion  28  composites the profile magnification of −20% and the color misregistration magnification of +2% to generate the composite magnification of −18.4%. In Block  1 , the pixel size is determined by the pixel size calculating portion  27  based on the composite magnification of −18.4%. Through insertion/extraction of bit data for each pixel based on the pixel size calculated as described above, the image data can be corrected to reduce the color misregistration of the image. 
     However, as in the first embodiment, the composite magnification correction is performed in synchronization with one pixel of the output image, and hence the corrected pixel position (first pixel position) of the composite magnification correction may be displaced from the corrected pixel position (second pixel position) of the profile magnification correction in some cases. When the profile magnification (correction amount) is large, the color misregistration may occur. To address this problem, in the second embodiment, the image data is corrected based on the displacement of the corrected pixel position between the composite magnification correction and the profile magnification correction.  FIG. 22  is a flowchart for illustrating image forming control operation based on the displacement of the corrected pixel position.  FIG. 23  is a block diagram of the image controller  20  based on the displacement of the corrected pixel position. The image controller  20  includes a CPU  21 , a memory  22 , an image data holding portion  24 , a profile magnification holding portion  25 , a color misregistration magnification holding portion  26 , a first pixel size calculating portion  51 , a second pixel size calculating portion  52 , a magnification compositing portion  28 , and an image signal output portion  29 . The CPU  21  executes the image forming operation as programmed by a program that is stored in the memory  22 . When the image forming control operation is started, the CPU  21  stores the image data in the image data holding portion  24 . The CPU  21  stores, in the profile magnification holding portion  25 , the profile magnification with respect to the scanning position X, which is obtained from the measurement result of the profile measuring device  40 . The CPU  21  stores, in the color misregistration magnification holding portion  26 , the color misregistration magnification obtained from the detection result of the pattern detectors  726 . 
     The CPU  21  determines whether a TOP signal  36  has been input to the first pixel size calculating portion  51  and the second pixel size calculating portion  52  (Step S 30 ). When the TOP signal  36  has been input (YES in Step S 30 ), the CPU  21  determines whether a BD signal  33  has been input to the first pixel size calculating portion  51  and the second pixel size calculating portion  52  (Step S 31 ). When the BD signal  33  has been input (YES in Step S 31 ), the first pixel size calculating portion  51  and the second pixel size calculating portion  52  read the profile magnification of the first pixel from the profile magnification holding portion  25  (Step S 32 ). The second pixel size calculating portion  52  calculates the pixel size based on the profile magnification (Step S 33 ). In other words, the second pixel size calculating portion  52  determines to what size one pixel is enlarged, reduced, or maintained in terms of the magnification. The second pixel size calculating portion  52  outputs the calculated pixel size to the profile magnification holding portion  25 . The CPU  21  determines whether output of one pixel corrected based on the profile magnification has been completed (Step S 34 ). When the output of one pixel corrected based on the profile magnification has been completed (YES in Step S 34 ), the CPU  21  determines whether output of image signals  31  corresponding to one line has been completed (Step S 35 ). When the output of the image signals  31  corresponding to one line has not been completed (NO in Step S 35 ), the processing returns to Step S 32 . The CPU  21  similarly corrects the pixel size of the next pixel based on the profile magnification. When the output of the image signals  31  corresponding to one line has been completed (YES in Step S 35 ), the CPU  21  determines whether the image formation has been completed (Step S 41 ). When the image formation has not been completed (NO in Step S 41 ), the processing returns to Step S 31 , and the image signals  31  for the next line are generated. 
     Meanwhile, in parallel to the correction of the pixel size based on the profile magnification by the second pixel size calculating portion  52  described above, the first pixel size calculating portion  51  reads the color misregistration magnification from the color misregistration magnification holding portion  26  (Step S 36 ). The first pixel size calculating portion  51  uses the magnification compositing portion  28  to calculate the composite magnification of the profile magnification and the color misregistration magnification with the use of Expression 4 (Step S 37 ). The first pixel size calculating portion  51  calculates the pixel size based on the image data, the composite magnification, and the error amount at the time when the previous one pixel size is determined (Step S 38 ). In other words, the first pixel size calculating portion  51  determines to what size one pixel is enlarged, reduced, or maintained in terms of magnification. The first pixel size calculating portion  51  outputs the calculated pixel size to the image signal output portion  29 . The image signal output portion  29  outputs, to the light source drive portion  18 , the image signal  31  corresponding to one pixel based on the calculated pixel size and the image data in the image data holding portion  24  (Step S 39 ). The light source drive portion  18  generates the drive signal  35  based on the image signal  31 , and outputs the drive signal  35  to the light source  10 . The light source  10  emits the light beam based on the drive signal  35  to form a latent image corresponding to one pixel on the photosensitive drum  708 . The CPU  21  determines whether output of image signals  31  corresponding to one line has been completed (Step S 40 ). When the output of the image signals  31  corresponding to one line has not been completed (NO in Step S 40 ), the processing returns to Step S 36 . The CPU  21  similarly corrects a pixel size of the next pixel. When the output of the image signals  31  corresponding to one line has been completed (YES in Step S 40 ), the CPU  21  determines whether the image formation has been completed (Step S 41 ). When the image formation has not been completed (NO in Step S 41 ), the processing returns to Step S 31 , and image signals  31  for the next line are generated. When the image formation has been completed (YES in Step S 41 ), the CPU  21  ends the image formation. 
       FIG. 24  is a diagram for illustrating magnifications and pixel sizes in continuous output operation of image signals  31 . A pixel size of one pixel without magnification correction is 100 bit data. The color misregistration magnification is +2%. The profile magnification is −25% for the first Block  0 , and −20% for the next Block  1 . The pixel size of the first pixel is changed, based on the profile magnification of −25% only, from 100 bit data to 75 bit data by the second pixel size calculating portion  52 . In this example, an error of less than 1 bit data is not generated by the correction based on the profile magnification only, and hence the next pixel size is calculated without an error. As a result, timing at which the second pixel size calculating portion  52  reads the profile magnification of the next pixel from the profile magnification holding portion  25  and calculates the pixel size of the next pixel based on the profile magnification only is when time corresponding to 75 bit data has elapsed. 
     In parallel to the calculation of the pixel size based on the profile magnification only by the second pixel size calculating portion  52 , the pixel size of the first pixel is determined as 77 bit data by the first pixel size calculating portion  51  based on the composite magnification of −23.5%. The pixel size is 76.5 bit data in calculation, but is determined as 77 bit data because the image signal  31  is output in units of 1 bit data. Therefore, an error of −0.5 bit data is generated. The error of −0.5 bit data is used when the pixel size of the next pixel is determined. As a result, timing at which the first pixel size calculating portion  51  reads the color misregistration magnification of the next pixel from the color misregistration magnification holding portion  26  and determines the pixel size based on the composite magnification is when time corresponding to 77 bit data has elapsed. 
     As described above, the timing at which the pixel size is calculated based on the composite magnification is displaced from the timing at which the pixel size is calculated based on the profile magnification only. As illustrated at around the center of  FIG. 24 , the profile magnification is changed when the block transitions from Block  0  to Block  1 . In this example, 76 bit data at the time when the block transitions from Block  0  to Block  1  is calculated based on the composite magnification of −23.5%. However, of 76 bit data, 12 bit data in Block  1  is to be determined based on the composite magnification of −18.4%. To address this problem, the first pixel size calculating portion  51  uses a displacement amount of the calculation timing of the pixel size as an error amount in the next calculation of the pixel size. The last pixel size of Block  0  illustrated in  FIG. 24  is calculated as 76 bit data with the use of 76.5 bit data determined from the composite magnification of −23.5% and the error of −0.5 bit data from the previous pixel. It is determined that there is no error amount for use in calculation of the pixel size of the next pixel, and the block of the profile magnification is switched from Block  0  to Block  1 . Based on the difference between the timing at which the pixel size is calculated based on the composite magnification (first timing) and the timing at which the pixel size is calculated based on the profile magnification only (second timing), only 12 bit data of 76 bit data is required to be corrected. 12 bit data is excessively reduced by 5.1% (=−18.4%−(−23.5%)) corresponding to the change of the composite magnification. In order to correct the excessive reduction, 0.6 bit data (=12 bit data×5.1%) is used as the error amount when the pixel size of the next pixel is calculated. 
     According to the second embodiment, the difference (displacement amount) between the first timing at which the pixel size is determined based on the profile magnification and the second timing at which the pixel size is determined based on the composite magnification can be used to correct the image data based on the composite magnification. Therefore, as in the first embodiment, the image with the reduced color misregistration can be formed. 
     According to the second embodiment, there can be reduced the color misregistration at the time when the profile magnification (first magnification) and the color misregistration magnification (second magnification) of the image in the main scanning direction are corrected in combination. 
     While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures and functions. 
     This application claims the benefit of Japanese Patent Application No. 2017-068629, filed Mar. 30, 2017, which is hereby incorporated by reference herein in its entirety.