Abstract:
An image forming apparatus includes a light source which illuminates in response to image data, and a deflector to deflect an optical beam output from the light source into a scanning beam running along a main scanning line across an image forming area in a main scanning direction. There are plurality of beam detectors to detect the scanning beam at a plurality of different positions along the main scanning line, the plurality of beam detectors including first and second beam detectors detecting the scanning beam at positions in front-end and rear-end sides, respectively, in the main scanning direction.

Description:
CROSS-REFERENCES TO RELATED APPLICATIONS 
     This application is a continuation application of U.S. application Ser. No. 11/857,505, filed Sep. 19, 2007 now abandoned, which claims priority to Japanese Patent Application No. 2006-252433, filed Sep. 19, 2006, the entire contents of which are incorporated herein by reference. This application is related to U.S. patent application Ser. No. 11/586,565 filed Oct. 26, 2006 and entitled “Image forming apparatus capable of effectively correcting main scanning misregistration”, which is incorporated herein by reference. The present invention may utilize any feature or technique set forth in application Ser. No. 11/586,565. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention generally relates to an optical apparatus and an image forming apparatus comprises the optical apparatus. 
     2. Discussion of the Background 
     A related art image forming apparatus such as a copying machine and a printer, for example, is generally provided with an optical device to produce an optical beam and uses it to write image information on a photoconductor. Such a related art image forming apparatus may employ a plastic lens to provide the optical beam to meet recent trends of reducing costs and weights, for example. In addition, the related art image forming apparatus has increasingly penetrated its market and expanded the range of uses and, as a consequence, it needs to satisfy the market demands for a higher accuracy of an image magnification in a variable magnification operation. 
     The related art image forming apparatus is generally configured to modulate the optical beam based on image data and to deflect the optical beam in a main scanning direction by a deflection mechanism (e.g., a polygon mirror) so as to make the optical beam scan a photoconductor surface through optical elements including an Fθ lens. 
     However, each of the related art image forming apparatuses may have a different main scanning magnification due to a variation in the optical device and/or properties of optical elements such as the Fθ. lens. A defective operation, for example, a magnification error or a misregistration of a writing start position, may also be generated by a change in a refractive index or a shape of the plastic lens and a change in a scanning position on the photoconductor caused by a variation in an environmental temperature or a variation in a temperature of the apparatus therein. Thereby, an image with a high quality may not be provided. When a related art color image forming apparatus for forming a color image by superimposing a plurality of color images issued, the defective operation, including the magnification error or the misregistration of the writing start position, may be generated in a color basis. Thereby, the main scanning magnification or writing start position for each color may need to be corrected. 
     JP 2003-279873A proposes to an image forming apparatus that comprises a light source to illuminate in response to image data, a deflector to deflect an optical beam output from the light source into a scanning beam running along a main scanning line across an image forming area in a main scanning direction, first and second beam detectors detecting the scanning beam at positions in front-end and rear-end sides at scanning line in the main scanning direction, a clock generator to generate writing clock signals for controlling an illumination of the light source, a measurement mechanism to measure period during a scanning period between detections of the scanning beam by the first and second beam detectors, a phase corrector to correct a phase of the writing clock signals based on correct amount that is set from measurement result. 
     JP2003-323085A proposes an image forming apparatus that comprises a plurality of beam detectors detecting the scanning beam at positions at scanning line in the main scanning direction, a clock generator to generate writing clock signals for controlling an illumination of the light source, a measurement mechanism to measure a count number of the writing clock signals generated during a scanning period between detections of the scanning beam by one beam detector and another beam detector by predetermined clock number (two position measurement), a main scanning magnification corrector to correct a main scanning magnification by the measurement mechanism and predetermined clock number. 
     But if an image forming apparatus uses the above phase correction technique and two position measurements for correcting a main scanning magnification, the image forming apparatus cannot correct a main scanning magnification strictly. This is because phase correction coverage is between front-end synchronous detecting position and rear-end image position. So the image forming apparatus cannot apply phase correction technique to between rear-end image position and rear-end synchronous detecting position, and the image forming apparatus has to use two different frequencies of writing clock signals. And the image forming apparatus counts writing clock signals between front-end synchronous detecting position and rear-end synchronous detecting position for correcting a main scanning magnification. So the frequency of writing clock signal changes while the image forming apparatus counts writing clock signals, the image forming apparatus cannot correct a main scanning magnification strictly. 
     SUMMARY OF THE INVENTION 
     The present invention provides an image reading apparatus which can correct a main scanning magnification, and the image forming apparatus controls a frequency of writing clock signals by counting the writing clock signals using a two position measurement technique. 
     An image forming apparatus according to the invention includes a light source, a deflector such as a rotating polygonal mirror, and front and rear beam detectors. Further, there is a clock generator which generates clock signals to control an illumination of a light source. There is a phase variable control unit which varies a phase of the writing clock signal. A measurement mechanism measures the scanning period between detections by the two beam detectors. A frequency corrector corrects a frequency of the writing clock signal so that a count number measured by the measurement mechanism becomes substantially equivalent to a predetermined referenced count number. A scanning period corrector corrects the scanning period at a scanning area where phase variable control is not available. 
     The invention also includes a method of correcting a scanning period. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic diagram illustrating an image forming apparatus according to an exemplary embodiment of the present invention; 
         FIG. 2  is a cross sectional view illustrating an optical device included in the image forming apparatus of  FIG. 1 ; 
         FIG. 3  is a schematic top view illustrating the optical device of  FIG. 2 ; 
         FIG. 4  is another schematic top view illustrating the optical device of  FIG. 2 ; 
         FIG. 5  is a block diagram illustrating a configuration of correcting a main scanning magnification by the optical device of  FIG. 2 ; 
         FIG. 6  is a block diagram illustrating a configuration of a writing clock generating unit included in  FIG. 5 ; 
         FIG. 7  is a flow chart showing the operation of the invention; and 
         FIG. 8  is a timing diagram showing the operation of the invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     In describing exemplary embodiments illustrated in the drawings, specific terminology is employed for the sake of clarity. However, the disclosure of this patent specification is not intended to be limited to the specific terminology so selected and it is to be understood that each specific element includes all technical equivalents that operate in a similar manner. Referring now to the drawings, wherein like reference numerals designate identical or corresponding parts throughout the several views, an image forming apparatus according to at least a first exemplary embodiment of the present invention is described. 
     Referring to  FIG. 1 , the image forming apparatus forming toner images of four colors, black, yellow, cyan, and magenta includes an optical device  1 , photoconductor drums  2 K,  2 Y,  2 C, and  2 M, an intermediate transfer belt  3 , intermediate transfer rollers  4 , development devices  5 K,  5 Y,  5 C, and  5 M, a belt cleaning device  6 , a transfer device  7 , a paper-feed registration sensor  8   a , a registration roller  8   b , a fixing device  9 , and an ejection device  10 . For a full color image forming apparatus, black, yellow, cyan, and magenta toner colors are respectively indicated using the suffixes K, Y, C, and M, and these color symbols may be omitted, as desired. 
     The image forming apparatus including the optical device  1  according to at least the first exemplary embodiment of the present invention employs a light source, for example, a laser diode, to irradiate surfaces of the photoconductor drums  2 K,  2 Y,  2 C, and  2 M with optical beams so as to form electrostatic latent images. This exemplary embodiment illustrates a full color image forming apparatus which forms a full color image by superimposing toner images of four colors. However, the invention is also applicable to a monochrome image forming apparatus. 
     The optical device  1  emits the laser beams to expose the surfaces of the photoconductor drums  2 K,  2 Y,  2 C, and  2 M. The photoconductor drum  2 K,  2 Y,  2 C, and  2 M form electrostatic latent images thereon by the laser beams emitted from the optical device  1 . The intermediate transfer belt  3  is an intermediate transfer member on which a toner image is transferred. The intermediate transfer rollers  4  rotate the intermediate transfer belt  3 . The development devices  5 K,  5 Y,  5 C, and  5 M develop the electrostatic latent images on the photoconductors  2 K,  2 Y,  2 C, and  2 M with toners. The belt cleaning device  6  removes remaining toner from the intermediate transfer belt  3 . The transfer device  7  transfers the toner image on the intermediate transfer belt  3  onto the transfer sheet. The paper-feed registration sensor  8   a  detects a leading end of the transfer sheet. The registration roller  8   b  registers the transfer sheet. The fixing device  9  fixes the toner image on the transfer sheet. The ejection device  10  ejects the transfer sheet on which the toner image is fixed. 
     The optical device  1  emits the optical beams at controlled timings so as to expose the photoconductors  2  when an image forming operation is requested from an operation unit (not shown) by a user or when a print start signal to start a print job is received from a host computer connected by a network or other type of wired or wireless connection. 
     A detailed description of the optical device  1  is provided with reference to  FIG. 2  though  FIG. 5 . Each of the development devices  5 K,  5 Y,  5 C, and  5 M forms a single color image on each of the respective photoconductor drums  2 K,  2 Y,  2 C, and  2 M which is rotated and exposed to the optical beam. When the photoconductor drums  2 K,  2 Y,  2 C, and  2 M have respective single color toner images formed thereon, the intermediate transfer belt  3  is rotationally driven by one of three intermediate transfer rollers  4 , for example, which is a drive roller. The belt  3  rotates in a direction B shown with an arrow in  FIG. 3  around two other intermediate transfer rollers  4  which are driven rollers. The single color images formed on the photoconductor drums  2 K,  2 Y,  2 C, and  2 M are sequentially transferred and superimposed onto the intermediate transfer belt  3  so that a full color image is formed on the intermediate transfer belt  3 . 
     When the print start signal is received, a paper-feed unit (not shown) separates one transfer sheet from a plurality of the transfer sheets so as to convey the one transfer sheet to the paper-feed registration sensor  8   a . When the one transfer sheet abuts, contacts, or is proximate to the paper-feed registration sensor  8   a , conveyance of the transfer sheet is stopped. The registration roller  8   b  is rotated at a desired timing so that the transfer sheet is fed between the intermediate transfer belt  3  and the transfer device  7 . Thereby, the full color image is transferred onto the transfer sheet by the transfer device  7 . 
     The transfer sheet on which the toner image is transferred by the transfer device  7  is conveyed to the fixing device  9  where heat and pressure are applied to fix the transferred image. The transfer sheet is ejected by an ejection roller included in the ejection device  10 , and is stacked on an ejection tray (not shown). The image forming apparatus of the exemplary embodiment forms the images of four colors by employing one optical device that is the optical device  1  while a related art optical device included in the related art image forming apparatus has four optical devices to form the images of four colors. A detailed description of the optical device  1  included in the image forming apparatus of  FIG. 3  is provided with respect to  FIG. 2  through  FIG. 5 . Referring to  FIG. 2 , the optical device  1  includes a polygon mirror  20 , fθ lenses  21   a  and  21   b , first mirrors  22 K,  22 Y,  22 C, and  22 M, curved axis toroidal lenses  23 K,  23 Y,  23 C, and  23 M, second mirrors  24 K,  24 Y,  24 C, and  24 M, and third mirrors  25 K,  25 Y,  25 C, and  25 M. The polygon mirror  20  is disposed in a center of the optical device  1 . This polygon mirror  20  deflects the optical beams used for the four colors in a main scanning direction. 
     Optical elements, for example, the fe lenses  21   a  and  21   b , the first mirrors  22 K,  22 Y,  22 C, and  22 M, the curved axis toroidal lenses  23 K,  23 Y,  23 C, and  23 M, the second mirrors  24 K,  24 Y,  24 C, and  24 M, and the third mirrors  25 K,  25 Y,  25 C, and  25 M, are disposed symmetrically to the central polygon mirror  20 . Because of this symmetrical disposition, optical paths for the optical beams of two colors are provided symmetrically so that the polygon mirror  20  deflects the optical beams of the four colors. As shown in  FIG. 3 , the optical paths for black and yellow are provided at a left side of the polygon mirror  20 , and the optical paths for cyan and magenta are provided at a right side of the polygon mirror  20 . 
     An operation of the optical device  1  will be given as follows. Laser diodes mounted in laser units  26 K,  26 Y,  26 C, and  26 M (shown in  FIG. 2 ) emit the optical beams towards cylindrical lenses  27 K,  27 Y,  27 C, and  27 M (shown in  FIG. 2 ). The cylindrical lenses  27 K,  27 Y,  27 C, and  27 M have respective desired refractive indexes in a sub-scanning direction so that the optical beams emitted from the laser units  26 K,  26 Y,  26 C, and  26 M are condensed in the sub-scanning direction, and are directed to a mirror side of the polygon mirror  20 . The polygon mirror  20  deflects the optical beams in the main scanning direction by high-speed rotations driven by a motor. The fθ lenses  21   a  and  21   b  are lenses to correct a scanning velocity of the laser beams. The first mirrors  22 K,  22 Y,  22 C, and  22 M reflect the optical beams deflected by the polygon mirror  20 . 
     After the optical beams reflected by the first mirrors  22 K,  22 Y,  22 C, and  22 M are directed to the curved axis toroidal lenses  23 K,  23 Y,  23 C, and  23 M, the optical beams are directed to the second mirrors  24 K,  24 Y,  24 C, and  24 M. The curved axis toroidal lenses  23 K,  23 Y,  23 C, and  23 M correct a property of the optical face angle error of the polygon mirror  20 . The optical beams reflected by the second mirrors  24 K,  24 Y,  24 C, and  24 M are reflected by the third mirrors  25 K,  25 Y,  25 C, and  25 M so that the optical beams exit from the optical device  1  in order to form electrostatic images on the respective photoconductors  2 K,  2 Y,  2 C, and  2 M. As stated above, the optical elements are disposed symmetrically to the central polygon mirror  20 , and the optical paths for the optical beams of two colors are provided symmetrically in the optical device  1  of the exemplary embodiment. 
     Referring to  FIG. 3 , a top view of the optical device  1  includes the polygon mirror  20 , the fθ lenses  21   a  and  21   b , the first mirrors  22 K,  22 Y,  22 C, and  22 M, the laser units  26 K,  26 Y,  26 C, and  26 M, the cylindrical lenses  27 K,  27 Y,  27 C, and  27 M, and reflection mirrors  28   a  and  28   b.    
     As stated above, the laser units  26 K,  26 Y,  26 C, and  26 M emit the optical beams from the laser diodes (not shown) so that the optical beams are directed towards the cylindrical lenses  27 K,  27 Y,  27 C, and  27 M. The cylindrical lenses  27 K,  27 Y,  27 C, and  27 M have respective desired refractive indexes in the sub-scanning direction so that the optical beams emitted from the laser units  26 K,  26 Y,  26 C, and  26 M are condensed in the sub-scanning direction. The reflection mirrors  28   a  and  28   b  may be used to reflect the optical beams so that the optical beams are directed towards the polygon mirror. When the polygon mirror  20  deflects the optical beams in the main scanning direction, the first mirrors  22 K,  22 Y,  22 C, and  22 M reflect the optical beams deflected by the polygon mirror  20  through the fθ lenses  21   a  and  21   b.    
     Referring to  FIG. 4 , another schematic top view of the optical device  1  is illustrated. The optical beams reflected in certain positions of the main scanning direction by the second mirrors  24 K,  24 Y,  24 C, and  24 M (shown in  FIG. 4 ) are reflected by synchronous detection reflection mirrors  29 K,  29 Y,  29 C, and  29 M towards synchronous detection lenses  30   a  and  30   b . Thereby, the optical beams are reflected to synchronous detection sensors  31   a  and  31   b . The synchronous detection lenses  30   a  and  30   b  condense the optical beams to the synchronous detection sensors  31   a  and  31   b . The synchronous detection sensors  31   a  and  31   b  are disposed symmetrically, and detect timings at which the optical beams of two colors are entered. In other words, the synchronous detection sensor  31   a  detects main scanning reference positions of cyan and magenta while the synchronous detection sensor  31   b  detects the black and yellow optical beams. 
     Referring to  FIG. 5 , a configuration of correcting a main scanning magnification in the optical device is illustrated using the laser unit  26 K as an example. As other laser units  26 Y,  26 C, and  26 M are configured to be the same as the laser unit  26 K, explanations for these laser units  26 Y,  26 C, and  26 M are omitted. 
     The optical beams emitted from the laser unit  26 K are deflected by the rotations of the polygon mirror  20 . As shown in  FIG. 7 , the deflected optical beams are received by the synchronous detection sensor  31   b  which is disposed outside an image area, expose the photoconductor drum  2 Y, and are received by a rear-end synchronous detection sensor  61  which is disposed outside the image area through the fθ lens  21   b  in a sequential manner. 
     When the synchronous detection sensor  31   b  and the rear-end synchronous sensor  61  receive the optical beams, these sensors respectively output to a writing clock generating unit  62 . This writing clock generating unit  62  determines or counts a number of clock signals generated between a time the optical beam is received by the synchronous detection sensor  31   b  and a subsequent time the optical beam is received by the rear-end synchronous detection sensor  61 , using the detection signals DETP_N and EDETP_N. The writing clock generating unit  62  stores a reference count number. This reference count number is measured or determined when the main scanning magnification is in an appropriate state. The writing clock generating unit  62  compares the measured count number and the reference count number, and corrects a writing clock frequency such that the measured count number is substantially equal to the reference count number (e.g., within 5%, 3%, 1%, 0.5%, 0.1%, or less, for example). The writing clock generating unit  62  outputs a writing clock signal CLK 0  based on the corrected writing clock frequency. The writing clock generating unit  62  outputs a plurality of clock signals as the writing clock signals CLK 0 , each of which has a different phase. As the writing clock generating unit  62  corrects the main scanning magnification by generating the writing clock signal, the writing clock generating unit  62  may be referred to as a magnification correction unit. 
     The writing clock signals CLK 0  output by the writing clock generating unit  62  are input to a phase synchronous unit  63 . The detection signal DETP_N output by the synchronous detection sensor  31   b  for every scanning of the optical beam is also input to the phase synchronous unit  63 . 
     Among the plurality of writing clock signals CLKO, the phase synchronous unit  63  selects one having a phase closest to a synchronous signal by comparing DETP_N with the writing clock signals CLKO. The clock signal selected by the phase synchronous unit  63  is output to a LD (laser diode) driver  55  as a writing clock signal CLK. The LD driver  55  causes the laser unit  26  to emit based on an image signal (referred to as an image data) and output the optical beam at a desired timing based on a synchronization to the writing clock signal CLK. 
     Referring to  FIG. 6 , a configuration of the writing clock generating unit  62  included in  FIG. 5  includes a counter  71 , a control unit  72 , and a clock generating unit  73 . The operation of these components is set forth with respect to  FIG. 7 . Referring to  FIG. 7 , when the detection signal DETP_N is input, the counter  71  begins to count a measurement clock signal ICLK. A count number of the measurement clock signal ICLK from when the detection signal DETP_N is input until the detection signal EDETP_N is input, is output to the control unit  72  (step  1 ). The counter  71  is cleared by the detection signal DETP_N. A count number output from the counter  71  represents a scanning period between the synchronous detection sensor  31   b  and the rear-end synchronous detection sensor  61   
     It is preferable to use writing clock signal CLK outputted from the phase synchronous unit  63  as a measurement clock signal ICLK. Because a signal that is synchronous with main scanning direction cycle makes the counter  71  reset, there is a reduced risk of miscount due to a phase difference between the synchronous detection sensor  31   b  and the rear-end synchronous detection sensor  61 . Moreover, the use of CLK as ICLK enables accurate counting of the clock signal between the synchronous detection sensor  31   b  and the rear-end synchronous detection sensor  61  by using the writing signal CLK that is substantially synchronous with synchronous detection signal of main scanning direction. 
     The control unit  72  calculates the frequency (f′=f×Rref/N) that corrects the writing clock frequency based on the count number N which is measured, etected, or determined, and the reference count number Rref and outputs data to the clock generating unit  73  (step  2 ). The reference count number Rref is a predetermined number. It is preferable that the count number, which is measured when precorrecting writing clock frequency operation occurs, is used as reference count number Rref, and a measurement clock signal, which is set when correcting writing clock frequency operation occurs, is used. And it is preferable that the reference count number Rref, which is referenced by the writing clock generating unit  62  when the writing clock generating unit  62  controls frequency, is measured when primary correcting writing clock frequency operation occurs. This is because the reference count number Rref enables a reduction in influence of variation in the optical device and/or properties of optical elements and corrects magnification correctly. 
     The control unit  72  corrects writing clock frequency based on the count number N which is measured and the reference count number Rref. If a writing clock frequency is f, and corrected writing clock frequency is F′, the control unit  72  can get corrected writing clock frequency by using below Equation 1.
 
 f′=f×R ref/ N   Equation 1
 
     The control unit  72  calculates the frequency based on the count number N which is measured between synchronous detection sensors  31   b  and a rear-end synchronous detection sensor  61  and which is substantially equivalent to a predetermined reference count number Rref. 
     The clock generating unit  73  generates clock signals CLK 0  which corresponds to f′ from the control unit  72  and outputs generated clock signals CLK 0  to the phase synchronous unit  63  (step  3 ). Main scanning magnification correction for Yellow, Cyan, and Magenta is the same as what has been described above for Black. 
     A PLL (phase locked loop) circuit is used for clock generating. But, the frequency generated by a PLL circuit is dispersed, so phase variable control that varies a phase of writing clock signals in units of 1/n of a writing clock cycle, where n is an integer of 2 or greater, at a position or a plurality of positions in the main scanning direction, may be used for slight adjustment of the clock generated by the PLL circuit. 
     
       
         
               
               
             
           
               
                   
               
               
                 It is preferable that the above slight 
                   
               
               
                 adjustment amount (phase variable 
               
               
                 amount) is listed and stored as de- 
               
               
                 scribed below. The slight adjustment 
                 Phase variable amount at 
               
               
                 amount is determined by the target 
                 area where phase variable 
               
               
                 writing clock frequency 
                 control is available 
               
               
                   
               
             
             
               
                 f1 
                 DN1 
               
               
                 f2 
                 DN2 
               
               
                 f3 
                 DN3 
               
               
                 f4 
                 DN4 
               
               
                 f5 
                 DN5 
               
               
                 f6 
                 DN6 
               
               
                 f7 
                 DN7 
               
               
                 f8 
                 DN8 
               
               
                 f9 
                 DN9 
               
               
                 F10 
                 DN10 
               
               
                 F11 
                 DN11 
               
               
                 F12 
                 DN12 
               
               
                 F13 
                 DN13 
               
               
                 F14 
                 DN14 
               
               
                 F15 
                 DN15 
               
               
                 F16 
                 DN16 
               
               
                 F17 
                 DN17 
               
               
                 F18 
                 DN18 
               
               
                 F19 
                 DN19 
               
               
                 F20 
                 DN20 
               
               
                 • 
                 • 
               
               
                 • 
                 • 
               
               
                 • 
                 • 
               
               
                   
               
               
                 • writing clock frequency 
               
             
          
         
       
     
       FIG. 8  shows there is an area where phase variable control is available and there is area where phase variable control is not available. If the image forming apparatus generates the writing clock signal using a PLL circuit and phase variable control, the counter  71  counts a measurement clock signal between detection signals DETP_N outputted by the synchronous detection sensor  31   b  and detection signals EDETP_N outputted by rear-end synchronous detection sensor  61 , by writing clock frequency: fpd generated by the PLL circuit and phase variable control at an area where phase correcting technique is available. The counter  71  also counts a measurement clock signal by writing clock frequency: fp generated by PLL at area where phase variable control is not available. The counter  71  counts a measurement clock signal using a different clock frequency at an area where phase variable control is available and an area where phase variable control is not available, so the image forming apparatus may not be able to completely correct the main scanning magnification. 
     The invention includes an image forming apparatus as described in the below three embodiments which can properly correct the main scanning magnification. 
     Embodiment 1 
     The control unit  72  stores a list or table as set forth below. The table has a phase variable amount DN′ at an area where phase variable control is not available. The phase variable amount DN′ is a predetermined ideal amount. 
     
       
         
               
               
               
             
           
               
                   
               
               
                 Writing clock 
                 Phase variable amount at 
                 Phase variable amount at 
               
               
                 signal 
                 area where phase variable 
                 area where phase variable 
               
               
                 frequency 
                 control is available 
                 control is not available 
               
               
                   
               
             
             
               
                 f1 
                 DN1 
                 DN′1 
               
               
                 f2 
                 DN2 
                 DN′2 
               
               
                 f3 
                 DN3 
                 DN′3 
               
               
                 f4 
                 DN4 
                 DN′4 
               
               
                 f5 
                 DN5 
                 DN′5 
               
               
                 f6 
                 DN6 
                 DN′6 
               
               
                 f7 
                 DN7 
                 DN′7 
               
               
                 f8 
                 DN8 
                 DN′8 
               
               
                 f9 
                 DN9 
                 DN′9 
               
               
                 f10 
                 DN10 
                 DN′10 
               
               
                 f11 
                 DN11 
                 DN′11 
               
               
                 f12 
                 DN12 
                 DN′12 
               
               
                 f13 
                 DN13 
                 DN′13 
               
               
                 f14 
                 DN14 
                 DN′14 
               
               
                 f15 
                 DN15 
                 DN′15 
               
               
                 f16 
                 DN16 
                 DN′16 
               
               
                 f17 
                 DN17 
                 DN′17 
               
               
                 f18 
                 DN18 
                 DN′18 
               
               
                 f19 
                 DN19 
                 DN′19 
               
               
                 f20 
                 DN20 
                 DN′20 
               
               
                 • 
                 • 
                 • 
               
               
                 • 
                 • 
                 • 
               
               
                 • 
                 • 
                 • 
               
               
                   
               
             
          
         
       
     
     The control unit  72  references the table to read the phase variable amount DN′ in accordance with the count number N and writing clock frequency fn that is measured as described above. The control unit  72  corrects the count number N based on phase variable amount DN′. If the corrected count number is N′, the coefficient for converting the phase variable amount DNn′ into count number is α, the control unit  72  can get the corrected count number N′ using Equation 2.
 
 N′=N+α×DNn′   Equation 2
 
     The control unit  72  can determine the corrected writing clock frequency using equation 1 and by using N′. Thus, the image forming apparatus can correct the main scanning magnification correctly. Because the control unit  72  can get the count number that is substantially the same count number that is measured by almost the same frequency between the detection signals DETP_N outputted by the synchronous detection sensor  31   b  and the detection signals EDETP_N the outputted by the rear-end synchronous detection sensor  61 . 
     For example, if N is 20000[ 1/16 dot], DNn′ is 10[¼ dot], α is 4, fn is 50.0 [MHz], Rref is 20200[ 1/16 dot], the control unit  72  can get corrected writing clock frequency f using Equation 3. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           f 
                           ′ 
                         
                         = 
                           
                         ⁢ 
                         
                           fn 
                           × 
                           
                             Rref 
                             / 
                             N 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           f 
                           × 
                           
                             Rref 
                             / 
                             
                               ( 
                               
                                 N 
                                 + 
                                 
                                   α 
                                   × 
                                   
                                     DNn 
                                     ′ 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           50.0 
                           × 
                           
                             20200 
                             / 
                             
                               ( 
                               
                                 20000 
                                 + 
                                 
                                   4 
                                   × 
                                   10 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           50.3992 
                           ⁢ 
                           
                               
                           
                           [ 
                           MHz 
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   3 
                 
               
             
           
         
       
     
     In this embodiment, the control unit  72  has a phase variable amount DN′. The control unit  72  can store values considered a instead of the phase variable amount DN′. 
     Embodiment 2 
     The control unit  72  calculates phase variable amount DN′ in accordance with the area where phase variable control is not available using DNn that is a phase variable amount at an area where phase variable control is available. If T 1  is a scanning period at an area where phase variable control is available, and T 2  is a scanning period at an area where a phase variable control is not available, the control unit  72  can calculate the phase variable amount DN′ using Equation 4.
 
 DNn′=DNn×T 2/T1  Equation 4
 
     The control unit  72  corrects the count number N by adding a result of DNn×T 2 /T 1 , if the writing clock frequency is fn and the coefficient for converting the phase variable amount DNn′ into count number is α. 
     The control unit  72  can get the corrected count number N′ using Equation 5.
 
 N′=N+α×DNn×T 2 /T 1  Equation 5
 
     The control unit  72  can get the corrected writing clock frequency using the above equation 1 by using N′. So, the image forming apparatus can correct the main scanning magnification correctly. Because the control unit  72  can get the count number that is substantially the same count number that is measured by almost same frequency between detection signals DETP_N outputted by the synchronous detection sensor  31   b  and detection signals EDETP_N outputted by rear-end synchronous detection sensor  61 . 
     For example, if N is 20000[ 1/16 dot], DNn is 200[¼ dot], α is 4, fn is 50.0 [MHz], Rref is 20200[ 1/16 dot], T 1  is 300 [μs], T 2  is 30 [μs], the control unit  72  can get the corrected writing clock frequency f using Equation 6. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           f 
                           ′ 
                         
                         = 
                           
                         ⁢ 
                         
                           fn 
                           × 
                           
                             Rref 
                             / 
                             N 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           f 
                           × 
                           
                             Rref 
                             / 
                             
                               ( 
                               
                                 N 
                                 + 
                                 
                                   α 
                                   × 
                                   
                                     . 
                                     DNn 
                                   
                                   × 
                                   T 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     2 
                                     / 
                                     T 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           50.0 
                           × 
                           
                             20200 
                             / 
                             
                               ( 
                               
                                 20000 
                                 + 
                                 
                                   4 
                                   × 
                                   200 
                                   × 
                                   
                                     30 
                                     / 
                                     300 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           50.2988 
                           ⁢ 
                           
                               
                           
                           [ 
                           MHz 
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   6 
                 
               
             
           
         
       
     
     Embodiment 3 
     The control unit  72  can correct the count number N by using fpd generated by the PLL circuit and phase variable control at an area where the phase correcting technique is available, and fp generated by PLL at an area where the phase variable control is not available. 
     The control unit  72  can get the corrected count number N′ using Equation 7.
 
 N′=N+T 2×( fpd−fp )  Equation 7
 
     The control unit  72  can get the corrected writing clock frequency using the above equation 1 by using N′. So, the image forming apparatus can correct main scanning magnification correctly. The control unit  72  can get the count number that is substantially the same count number that is measured by almost the same frequency between detection signals DETP_N outputted by the synchronous detection sensor  31   b  and detection signals EDETP_N outputted by the rear-end synchronous detection sensor  61 . 
     For example, if N is 20000[ 1/16 dot], DNn is 200[¼ dot], β is 16, Rref is 20200[ 1/16 dot], T 2  is 30 [μs], fdp is 50.0 [MHz], fp is 49.0 [MHz], the control unit  72  can get the corrected writing clock frequency f using Equation 8. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           f 
                           ′ 
                         
                         = 
                           
                         ⁢ 
                         
                           fpd 
                           × 
                           
                             Rref 
                             / 
                             N 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           f 
                           × 
                           
                             Rref 
                             / 
                             
                               ( 
                               
                                 N 
                                 + 
                                 
                                   β 
                                   × 
                                   T 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                   × 
                                   
                                     ( 
                                     
                                       fpd 
                                       - 
                                       fp 
                                     
                                     ) 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           50.0 
                           × 
                           
                             20200 
                             / 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           ( 
                           
                             20000 
                             + 
                             
                               16 
                               × 
                               30 
                               × 
                               
                                 10 
                                 
                                   - 
                                   6 
                                 
                               
                               × 
                               
                                 ( 
                                 
                                   50.0 
                                   - 
                                   49.9 
                                 
                                 ) 
                               
                               × 
                               
                                 10 
                                 6 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           50.2988 
                           ⁢ 
                           
                               
                           
                           [ 
                           MHz 
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   8 
                 
               
             
           
         
       
     
     The main scanning magnification correction for Yellow, Cyan, and Magenta is the same as the above mentioned main scanning magnification correction for Black. 
     This invention is applicable to mono-color image forming apparatuses, and also plural color image forming apparatuses. 
     Obviously, numerous additional modifications and variations of the present invention are possible in light of the above teachings. It is therefore to be understood that within the scope of the appended claims, the present invention may be practiced otherwise than as specifically described herein.