Abstract:
An image forming apparatus using a two-component developer includes a sensor mechanism, an image forming mechanism, a toner supply controller, a memory, an estimation mechanism, and a correction mechanism. The sensor mechanism detects a toner density of the developer. The image forming mechanism produces a toner image at one of at least two selectable process linear speeds. The toner supply controller controls a toner amount based on a result by the sensor mechanism. The memory stores data of an external input voltage for adjusting a variation in an output voltage of the sensor mechanism. The estimation mechanism estimates a difference between output voltages of the sensor mechanism before and after a speed selection of the at least two linear speeds is changed. The correction mechanism corrects the output voltage of the sensor mechanism when a speed selection of the at least two selectable process linear speeds is changed.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
   This patent specification is based on Japanese patent application, No. 2005-304475 filed on Oct. 19, 2005 in the Japan Patent Office, the entire contents of which are incorporated by reference herein. 
   BACKGROUND 
   1. Field of Invention 
   Exemplary aspects of the present invention relate to a method and apparatus for image forming, and more particularly, to a method and apparatus for image forming capable of effectively correcting an output from a toner density sensor. 
   2. Description of the Related Art 
   A related art image forming apparatus has employed a two-component development method commonly known in the art. This two-component development method develops an image by carrying a two-component developer (hereafter referred to as a developer) including a non-magnetic toner and a magnetic carrier on a development sleeve as a developer carrier, forming the developer in a magnetic-brush-like shape on the development sleeve by an action of magnetic poles included in the development sleeve, and applying a development bias to the development sleeve at a location opposing to a photoconductor as a latent image carrier. This two-component development method is advantageous in color image forming and, consequently, has been widely employed. In the two-component development method, the developer is carried to a development region with a rotation of the development sleeve. According to this movement of the developer, a large amount of the magnetic carriers in the developer are gathered with attached toner particles along lines of magnetic force of the development poles so that the developer is formed in a magnetic-brush-like shape. 
   Unlike a one-component development method, the two-component development method is believed to be important to efficiently control a weight ratio (referred to as a toner density) between a toner and the carrier to enhance stability. For example, when the toner density is excessively high, a background soiling is generated on the image, and a detail resolving power is decreased. When the toner density is low, deterioration of a solid image density or adhesion of the carrier is generated. Thereby, the toner quantity supplied to the developer is controlled, and the toner density in the developer needs to be controlled within an appropriate range. The toner density is controlled by comparing an output value Vt of a permeability sensor, serving as a toner density detection mechanism, with a reference value Vref density, and arranging the toner supply quantity based on a result of the comparison. 
   The permeability sensor is generally used to detect the toner density as permeability. The sensor detects a permeability variation of the developer caused by a variation of the toner density of the developer, and compares the output of the sensor with the reference density so as to determine the current value of the toner density. Another method uses an optical sensor toner density. The result detected by the optical sensor detects a reflection density of an image area and a non-image area of a reference pattern, which is formed on an image carrier or an intermediate transfer belt, so as to determine the toner density. 
   Another publicly known method is to control the reference value Vref of the permeability sensor based on a detection result of a toner adhesion amount of the reference pattern, which is formed between each of image outputs (between sheets), even during image forming operation. However, when the reference pattern is formed between the sheets, the toner is excessively consumed. This excess consumption of the toner needs to be reduced. Thereby, there is a tendency not to control the Vref by forming the reference pattern between the sheets. When the reference pattern is formed on the intermediate transfer belt, a cleaning device needs to be disposed on a secondary transfer roller. Thereby, there is a tendency not to form the reference pattern between the sheets from a cost reduction point of view. In such a case, the toner density needs to be correctly controlled by the permeability sensor solely when the images are continuously formed or an image mode is changed, such as the process linear velocity. 
   One example has attempted to detect the toner density of the developer in a development device by using the permeability sensor as the toner density detection mechanism, comparing a result detected by the permeability sensor with a threshold value, controlling the toner density in the development device based on a result of the comparison, and changing the threshold value with respect to a detection value of the toner density detection mechanism in response to a variation of a photoconductor linear velocity. 
   SUMMARY 
   An image forming apparatus using a two-component developer having toner and carriers includes a sensor mechanism, an image forming mechanism, a toner supply controller, a memory, an estimation mechanism, and a correction mechanism. The sensor mechanism is configured to detect a toner density of the developer. The image forming mechanism is provided with at least two selectable process linear speeds and configured to produce a toner image at one of the selectable process linear speeds. The toner supply controller is configured to control an amount of toner to be supplied to the image forming mechanism based on a detection result of the toner density by the sensor mechanism. The memory is configured to store data of an external input voltage for adjusting a variation in an output voltage of the sensor mechanism. The estimation mechanism is configured to estimate, based on the data of the external input voltage stored in the memory, a difference between output voltages of the sensor mechanism before and after a speed selection of the at least two selectable process linear speeds is changed from one to another. The correction mechanism is configured to correct the output voltage of the sensor mechanism when the selection of the at least two selectable process linear speeds is changed from one to another based on the difference between the output voltages of the sensor mechanism before and after the speed selection, which is estimated by the estimation mechanism. 
   In another embodiment, an image forming method using at least two selectable process linear speeds and forming a toner image at one of the at least two selectable process linear speeds selected by using a two-component developer including toner and carriers is carried out by the following steps: (1) providing a sensor mechanism for sensing a toner density of the developer; (2) storing data of an external input voltage for adjusting a variation in an output voltage of the sensor mechanism; (3) estimating, based on the data of the external input voltage stored by the storing step, a difference between output voltages of the sensor mechanism before and after a speed selection of the at least two selectable process linear speeds is changed from one to another; and (4) correcting the output voltage of the sensor mechanism when the selection of the at least two selectable process linear speeds is changed from one to another based on the difference between the output voltages of the sensor mechanism before and after the speed selection estimated by the estimating step. 
   An image forming apparatus provided with at least two selectable process linear speeds and forming a toner image at one of the at least two selectable process linear speeds selected with using a two-component developer includes a sensor mechanism, a memory, a means for estimating, and a means for correcting. The sensor mechanism is used for sensing a toner density of the developer. The memory is used for storing data of an external input voltage for adjusting a variation in an output voltage of the sensor mechanism. The means for estimating may be performed based on the data of the external input voltage stored by the storing step, a difference between output voltages of the sensor mechanism before and after a speed selection of the at least two selectable process linear speeds is changed from one to another by applying a quadratic approximation formula with respect to the data of the external input voltage. The means for correcting the output voltage of the sensor mechanism may be performed when the selection of the at least two selectable process linear speeds is changed from one to another based on the difference between the output voltages of the sensor mechanism before and after the speed selection estimated by the means for estimating the difference. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     A more complete appreciation of the exemplary aspects of the invention and many of the attendant advantages thereof will be readily obtained as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings, wherein: 
       FIG. 1  is a cross sectional view illustrating an image forming apparatus according to an exemplary embodiment of the present invention; 
       FIG. 2  is an enlarged cross sectional view illustrating a process cartridge included in the image forming apparatus of  FIG. 1 ; 
       FIG. 3  is a block diagram illustrating a portion of an electric circuit for the image forming apparatus of  FIG. 1 ; 
       FIG. 4  is a schematic diagram illustrating reference patterns of two colors on an intermediate transfer belt included in the image forming apparatus of  FIG. 1 ; 
       FIG. 5  is a graph showing a relationship between a detection voltage with respect to a reference image patch of a photo sensor and a toner adhesion amount of the reference image patch in the exemplary embodiment; 
       FIG. 6  is a graph showing a relationship between a development potential and a toner adhesion amount of the reference pattern in the exemplary embodiment; 
       FIG. 7  is a graph showing a relationship between an external input voltage value at which a permeability sensor is read and a shift amount of an output from the permeability sensor at which a process linear velocity is switched; and 
       FIG. 8  is a schematic circuit diagram illustrating a configuration of the permeability sensor used in the exemplary embodiment. 
   

   DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
   In describing the 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 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 first exemplary embodiment of the present invention is described. 
   Referring to  FIG. 1 , the image forming apparatus  100  forming a toner image on a transfer sheet with an electrophotographic method includes process cartridges (also referred to as toner image forming units)  6 Y,  6 M,  6 C, and  6 K, an optical writing unit  7 , a sheet feeding mechanism  200 , a pair of registration rollers  28 , an intermediate transfer unit  15 , a secondary transfer roller  19 , a fixing device  20 , a pair of ejection rollers  29 , a stacking area  30 , toner bottles  32 Y,  32 M,  32 C, and  32 K, and a reflective photo sensor  40 . The process cartridges  6 Y,  6 M,  6 C, and  6 K respectively include photoconductors  1 Y,  1 M,  1 C, and  1 K as latent image carriers. The symbols Y, M, C, and K respectively indicate toner colors of yellow, magenta, cyan, and black, and these symbols may be omitted as necessary. The sheet feeding mechanism  200  includes a feeding roller  27  and a sheet cassette  26  in which a transfer sheet  201  is stored. The intermediate transfer unit  15  includes an intermediate transfer belt  8  as an intermediate transfer member, primary transfer bias rollers  9 Y,  9 M,  9 C, and  9 K, a cleaning device  10 , a secondary transfer backup roller  12 , a cleaning backup roller  13 , and a tension roller  14 . 
   The process cartridges  6 Y,  6 M,  6 C, and  6 K are removable and respectively form the toner images of yellow, magenta, cyan and black (referred to as Y toner image, M toner image, C toner image, and K toner image). A detailed description of one of the process cartridges will be given with  FIG. 2 . 
   The optical writing unit  7  as an exposure device applies laser lights on the photoconductors  1 Y,  1 M,  1 C,  1 K on which electrostatic latent images are formed. The sheet cassette  26  and the feeding roller  27  of the sheet feeding mechanism  200  respectively stores a plurality of the transfer sheets  201  therein, and feeds the transfer sheet  201  towards the registration rollers  28 . The pair of registration rollers  28  register the transfer sheet  201  so as to feed the sheet  201  towards a secondary transfer nip area which will be described later at an appropriate timing. 
   The intermediate transfer unit  15  forms the toner image onto the intermediate transfer belt  8 . A detailed description of the intermediate transfer unit  15  will be given later. The secondary transfer roller  19  transfers the toner images onto the transfer sheet  201 . The fixing device  20  fixes the toner image on the transfer sheet  201 . The pair of ejection rollers  29  eject the transfer sheet  201  with the fixed image to the stacking area  30 . The stacking area  30  is a place to stack the transfer sheet  201  ejected from the pair of ejection rollers  20 . The toner bottles  32 Y,  32 M,  32 C, and  32 K store toners of yellow, magenta, cyan, and black respectively. The reflective photo sensor  40 , as an image density detection mechanism, detects a density of the intermediate transfer belt  8  so as to output a signal in correspondence to an optical reflectance of the transfer belt  8 . For the reflective photo sensor  40 , among a diffusion light detection type and a regular reflection light detection type, a reflective photo sensor capable of providing an adequate value from a difference between a reflected light quantity of a surface of the intermediate transfer belt  8  and a reflected light quantity of a reference pattern image (described later) is employed. 
   In an image forming operation, the optical writing unit  7  emits a plurality of laser lights based on each image information of the toner colors Y, M, C, and K, and irradiates the photoconductors  1 Y,  1 M,  1 C, and  1 K included in the respective process cartridges  6 Y,  6 M,  6 C, and  6 K so as to form the electrostatic latent images on the respective photoconductors  1 Y,  1 M,  1 C, and  1 K. The optical writing unit  7  irradiates the photoconductors  1 Y,  1 M,  1 C, and  1 K through a plurality of optical lenses or mirrors while scanning deflectively a plurality of laser light sources by a polygon mirror, which is rotationally driven by a motor. 
   The sheet cassette  26  included in the sheet feeding mechanism  200  stores the plurality of the transfer sheets  201  so that each transfer sheet  201  is stacked on top of the one below. The feeding roller  27  abuts on one of the transfer sheets  201  stacked on the very top. When the feeding roller  27  is rotated by a drive mechanism (not shown) in a counterclockwise direction, the transfer sheet  201  stacked on the very top in the sheet cassette  26  is fed by the feeding roller  27  and conveyed to the registration rollers  28 . The registration rollers  28  are driven rotationally so as to nip the transfer sheet  201 . However, the registration rollers  28  stop immediately after the transfer sheet  201  is nipped. Then, the registration rollers  28  start moving to feed the transfer sheet  201  towards the secondary transfer nip area at the appropriate timing. 
   The intermediate transfer unit  15  is disposed such that the intermediate transfer belt  8  in an endless belt shape is laid across the secondary transfer backup roller  12 , cleaning backup roller  13 , and tension roller  14  in a tensioned condition. The intermediate transfer belt  8  is moved in a counterclockwise direction by at least one of the secondary transfer backup roller  12 , cleaning backup roller  13 , and tension roller  14  rotationally driven by a rotation driving unit. 
   The intermediate transfer belt  8  is nipped in primary transfer nip areas formed between the primary transfer bias rollers  9 Y,  9 M,  9 C, and  9 K and the respective photoconductors  1 Y,  1 M,  1 C, and  1 K. The primary transfer bias rollers  9 Y,  9 M,  9 C, and  9 K apply toner biases applied from a high voltage power source (not shown) to a backside (an inside circumference surface) of the intermediate transfer belt  8 . The toner biases applied from the power source have reverse polarity against the toner. For example, the toner biases with plus polarity are applied from the power source. The secondary transfer backup roller  12 , cleaning backup roller  13 , and tension roller  14  are electrically grounded while the primary transfer bias rollers  9 Y,  9 M,  9 C, and  9 K are not grounded. The toner images of the yellow, magenta, cyan, and black on the respective photoconductors  1 Y,  1 M,  1 C, and  1 K are primarily transferred onto the intermediate transfer belt  8  in a process in which the intermediate transfer belt  8  sequentially passes the respective primary transfer nip areas. Thereby, a full color image is formed onto the intermediate transfer belt  8  by superimposing the images of the four colors. 
   The secondary transfer backup roller  12  and the secondary transfer roller  19  form the secondary nip area therebetween. The secondary transfer roller  19  is applied with the transfer bias from the high voltage power source (not shown). In the secondary transfer nip area, the full color image formed by superimposing the toner images of four colors onto the intermediate transfer belt  8  is transferred on the transfer sheet  201  fed from the registration roller  28 . After the intermediate transfer belt  8  passes the secondary nip area, the cleaning device  10  removes a remaining toner which is not transferred on the transfer sheet  201  from the transfer belt  8 . In the secondary transfer nip area, the transfer sheet  201  is nipped between the intermediate transfer belt  8  and the secondary transfer roller  16  both surfaces of which move in a forward direction, and is conveyed to a direction opposing to the registration rollers  28 . The transfer sheet  201  fed from the secondary transfer nip area is conveyed to the fixing device  20  in which the full color toner image on the transfer sheet  201  is fixed by heat and pressure. After the full color image is fixed, the transfer sheet  201  is ejected to the stacking area  30  by the ejection rollers  29 . 
   As shown in  FIG. 1 , the optical writing unit  7  and the intermediate transfer unit  15  are disposed respectively below and above the process cartridges  6 Y,  6 M,  6 C, and  6 K. The sheet feeding mechanism  200  is disposed below the optical wiring unit  7 . The reflective photo sensor  40  is disposed above the secondary transfer backup roller  12 , and a detail description thereof will be given later. 
   Referring to  FIG. 2 , since the process cartridges  6 Y,  6 M,  6 C, and  6 K included in  FIG. 1  are configured to be the same except for the toner colors, one of the process cartridges  6 Y,  6 M,  6 C,  6 K is illustrated as an example process cartridge  6 . The color symbols Y, M, C, and K indicating yellow, magenta, cyan, and black are omitted as necessary. The process cartridge may be replaced with a new one at the end of the lifetime thereof. 
   As shown in  FIG. 2 , the process cartridge  6  generating the toner image includes the photoconductor  1 , a drum cleaner  2 , a charging device  4 , a development device  5  and a discharge device (not shown). The development device  5  includes a development sleeve  51 , a control member  52 , a two-component developer  53 , a development container  54 , and an agitation conveyance member  55 . 
   The photoconductor  1  forms the electrostatic latent image thereon by the laser light applied by the optical writing unit  7  as described with  FIG. 1 . The laser light is indicated by a letter L in  FIG. 2 . The photoconductor  1  is rotated in a clockwise direction by a driving mechanism (not shown). 
   The charging device  4  uniformly charges a surface of the photoconductor  1 . When the surface of the photoconductor  1  is uniformly charged, the laser light emitted from the optical writing unit  7  (see  FIG. 1 ) based on the image information scans the surface of the photoconductor  1 . Thereby, the electrostatic latent image is formed on the surface of the photoconductor  1 . This electrostatic latent image on the photoconductor  1  is developed by the development device  5  including the two-component developer  53  so as to form the toner image. This two-component developer  53  includes a non-magnetic toner and a magnetic carrier. The primary transfer bias roller  9  is applied with the transfer bias from the high voltage power source (not shown), and a transfer electric field is formed between the primary transfer bias roller  9  and the photoconductor  1 . The toner image on the photoconductor  1  is transferred on the intermediate transfer belt  8  by the transfer electric field. 
   The drum cleaner  2  removes a remaining toner from the surface of the photoconductor  1  on which an intermediate transfer process is undergone. The discharge device (not shown) discharges a residual charge of the photoconductor  1  after the drum cleaner  2  removes the remaining toner. The discharge process by the discharge device causes the surface of the photoconductor  1  to initialize for the next image forming operation. 
   The development device  5  develops the electrostatic latent image on the photoconductor  1  to form the toner image. In the development device  5 , the agitation conveyance member  55  agitates and conveys the two-component developer  53  having the non-magnetic toner and the magnetic carrier, and the development sleeve  51  as a developer carrying member includes a magnetic pole therein which forms a magnetic brush. The development container  54  supports the agitation conveyance member  55 . The agitation conveyance member  55  and the development sleeve  51  are rotationally driven by a rotation driving device (not shown). When a process linear velocity of the image forming apparatus is changed, rotation speeds of the agitation conveyance member  55  and the development sleeve  51  are changed by the rotation driving device (not shown). The development device  5  has a permeability sensor  56  (hereafter referred to as a P sensor  56 ) as a toner density sensor disposed below thereof. This P sensor  56  detects the toner density (also referred to as a permeability) in the development device  5 , and is controlled by a control unit  150  which will be described in  FIG. 3 . As shown in  FIG. 2 , the control unit  150  is connected with a toner supply motor  41  which supplies a toner from the toner bottle  32  (shown as  32 Y,  32 M,  32 C, and  32 K in  FIG. 1 ). The developer  53  on the development sleeve  51  is conveyed to a development area with a rotation of the development sleeve  51 . As the developer  53  is conveyed to the development area, a plurality of the magnetic carriers in the developer  53  are gathered with the toner along with a magnetic line of force of a development pole so as to form the magnetic brush. The control member  52  controls a thickness of the developer  53  on the development sleeve  51 . The development sleeve  51  is applied with the development bias from the high voltage power source at a location opposing to the photoconductor  1  so that the electrostatic latent image on the photoconductor  1  is developed by adhering the toner in the developer on the development sleeve  51 . 
   Therefore, the process cartridges  6 Y,  6 M,  6 C, and  6 K (shown as  6  in  FIG. 2 ) respectively include the photoconductors  1 Y,  1 M,  1 C, and  1 K shown in  FIG. 1 , the drum cleaners  2 Y,  2 M,  2 C, and  2 K (shown as  2  in  FIG. 2 ), discharge devices (not shown), charging devices  4 Y,  4 M,  4 C, and  4 K (shown as  4  in  FIG. 2 ), and development devices  5 Y,  5 M,  5 C, and  5 K (shown as  5  in  FIG. 2 ). These process cartridges  6 Y,  6 M,  6 C, and  6 K respectively form the Y, M, C, and K toner images on the photoconductors  1 Y,  1 M,  1 C, and  1 K. The Y, M, C, and K toner images are superimposed and transferred on the intermediate transfer belt  8  by the respective primary transfer bias rollers  9 Y,  9 M,  9 C, and  9 K shown in  FIG. 1  (also shown as  9  in  FIG. 2 ) so as to form the full color image. The development device  5 Y,  5 M,  5 C, and  5 K respectively include development sleeves  51 Y,  51 M,  51 C, and  51 K (shown as  51  in  FIG. 2 ), developers  53 Y,  53 M,  53 C, and  53 K (shown as  53  in  FIG. 2 ), and toner supply motors  41 M,  41 M,  41 C, and  41 K (shown as  41  in  FIG. 2 ). 
   Referring to  FIG. 3 , a portion of an electric circuit of the image forming apparatus includes the control unit  150 . The control unit  150  includes a central processing unit (CPU)  150   a  to control, for example, a computation unit, and a random access memory (RAM)  150   b  to store data. This control unit  150  controls, for example, process cartridges  6 Y,  6 M,  6 C, and  6 K, the optical writing unit  7 , the sheet cassette  26 , the pair of registration rollers  28 , the intermediate transfer unit  15 , the reflective photo sensor  40 , and the permeability sensors  56 Y,  56 M,  56 C, and  56 K, each of which is electrically connected. 
   The control unit  150  examines an image forming capability, for example, the image forming capability of each process cartridge  6 Y,  6 M,  6 C, and  6 K at a predetermined timing, for example, when a main power source (not shown) of the image forming apparatus is activated, during standby after a predetermined time period is passed from the activation of the main power source, or during standby after the images are formed on at least a predetermined number of sheets. Thereby, the control unit  150  controls the toner supply quantity to the development devices  5 Y,  5 M,  5 C, and  5 K from respective toner supply devices during sheet feeding. 
   Specifically, the control unit  150  reads the photo sensor  40  when the predetermined timing is provided. During the reading of the photo sensor  40 , the control unit  150  sequentially changes a light emitting quantity of the photo sensor  40  while being in a non-image forming state so as to determine the light emitting quantity at which a detection voltage of the photo sensor becomes 4.0V±0.2V. The control unit  150  uses the light emitting quantity when the toner adhesion amount of the pattern image is detected. The control unit  150  controls a motor which rotates the photoconductors  1 Y,  1 M,  1 C, and  1 K, and causes the charging devices  4 Y,  4 M,  4 C, and  4 K to uniformly charge the photoconductors  1 Y,  1 M,  1 C, and  1 K while rotating the photoconductors. This charging operation differs from a uniform charging process, for example, −700V charging, during a normal image forming operation. In other words, the control unit  150  controls the high voltage power source which applies the voltage to the charging devices  4 Y,  4 M,  4 C, and  4 K such that charging potentials of photoconductors  1 Y,  1 M,  1 C, and  1 K are gradually increased. While the control unit  150  controls the optical writing unit  7  to form the electrostatic latent images for the reference pattern images on the photoconductors  1 Y,  1 M,  1 C, and  1 K by scanning with the laser light, the electrostatic latent images for the reference pattern images on the photoconductors  1 Y,  1 M,  1 C, and  1 K are developed by the development devices  5 Y,  5 M,  5 C, and  5 K. Thereby, the reference pattern images of yellow, magenta, cyan, and black are formed on the respective photoconductors  1 Y,  1 M,  1 C, and  1 K. 
   In a course of the development process, the control unit  150  controls the high voltage power source such that the development biases applied from the high voltage power source to the development sleeves  51 Y,  51 M,  51 C, and  51 K in the respective development devices  5 Y,  5 M,  5 C, and  5 K are gradually increased. In this manner, the reference pattern image is formed by forming a plurality of reference image patches from a low image density to a higher image density. In other wards, image densities of the plurality of reference image patches in the reference pattern image are gradually increased. A method for forming the reference pattern image will be described later. 
   On the other hand, when both the charging potentials and development biases of the photoconductors  1 Y,  1 M,  1 C, and  1 K are gradually decreased, the reference image patches in the reference pattern image are formed from a high image density to a lower image density. However, as the high voltage power source generally consumes a more time reducing a voltage than increasing the voltage, a time necessary to form the reference pattern images may be extended. 
   The reference pattern images on the respective photoconductors  1 Y,  1 M,  1 C, and  1 K are transferred to be sided one another onto the transfer belt  8 , not to be superimposed one on another. When each reference pattern image passes the location opposing to the photo sensor  40  with a movement of the intermediate transfer belt  8 , each thereof reflects the light emitted from the reflective photo sensor  40 , and a reflected light quantity reflected by each reference pattern image is detected by the reflective photo sensor  40  so as to be output to the control unit  150  as an electric signal. The control unit  150  computes an optical reflectance of each of the plurality of reference image patches based on an output value of the reflective photo sensor  40  sequentially transmitted from the reflective photo sensor  40  in corresponding to detection of the reflected light quantity of each reference image patch in the reference pattern image on the intermediate transfer belt  8 . The control unit  150  stores data of the optical reflectance computed for each reference image patch in the RAM  150   a  as density pattern data. When the reference pattern images on the intermediate transfer belt  8  pass through the location opposing to the reflective photo conductor  40 , the reference pattern images are removed by the cleaning device  10 . 
   Referring to  FIG. 4 , the reference pattern images on the intermediate transfer belt  8  are illustrated. As shown in  FIG. 4 , the reference pattern images of black and cyan are respectively indicated as Pk and Pc as examples. The reference pattern image of yellow (Py) or magenta (Pm) is not shown in  FIG. 4 , however, configuration thereof is the same as that of black or cyan. Each reference pattern image includes 10 reference image patches. For example, the reference pattern image Pk includes 10 reference image patches Pk 1  through Pk 10 , and the reference pattern image Pc includes 10 reference image patches Pc 1  through Pc 10 . These 10 reference image patches are formed and sided 13 mm away from one another on the intermediate transfer belt  8 , and each reference image patch is sized at 13 mm×15 mm according to the image forming apparatus. Thereby, each reference pattern image Pk, Pc, Py, and Pm having the respective 10 reference image patches has a length L 2  that is 247 mm. Unlike the full color toner image formed by superimposing the toner image of one color on another, the reference pattern images Pk, Pc, Py, and Pm are formed at appropriate timings so as to be sided and transferred on the intermediate transfer belt  8  without superimposition. 
   As shown in  FIG. 4 , the reflective photo sensor  40  is disposed above in the intermediate transfer unit  15  which includes the intermediate transfer belt  8 . After the reflective photo sensor  40  detects each reference pattern image on the intermediate transfer belt  8  with the movement of the intermediate transfer belt  8 , the cleaning device  10  removes each reference pattern image from the intermediate transfer belt  8 . The reflective photo sensor  40  detects the reflected light quantity from each of the plurality of reference image patches included in the reference pattern images Pk, Pc, Pm, (not shown) and Py (not shown). In other words, the reflective photo sensor  40  sequentially detects densities for the 10 reference image patches Pk 1  through Pk 10  included in the reference pattern image Pk, the 10 reference image patches Pc 1  through Pc 10  included in the reference pattern image Pc, the 10 reference image patches Pm 1  through Pm 10  included in the reference pattern image Pm, and the 10 reference image patches Py 1  through Py 10  included in the reference pattern image Py. In this case, the reflective photo sensor  40  detects the reflected light quantity of each reference image patch, and sequentially outputs the signal to the control unit  150  (shown in  FIG. 3 ) based on the reflected light quantity. The control unit  150  sequentially computes the image density of each reference image patch, and stores in the RAM  150   b  (shown in  FIG. 3 ) based on the signals sequentially transmitted from the reflective photo conductor  40 . 
   The image density of each reference image patch is converted into the toner adhesion amount by a conversion method. According to the conversion method, the control unit  150  converts detection outputs of the reference pattern image Pk, Pc, Pm, and Py having respective 10 reference image patches from the reflective photo sensor  40  into toner adhesion amount data of the reference image patches based on a relationship between a detection voltage of the reflective photo sensor  40  respect to the reference image patches and the toner adhesion amount of the reference image patches (the toner density of the developer) shown in  FIG. 5 . The control unit  150  stores the toner adhesion amount data converted from the image density in the RAM  150   b . A detailed description of  FIG. 5  will be given later. The control unit  150  stores the toner adhesion amount data in the RAM  150   b  while estimating the development potentials of the reference pattern images based on an image forming condition of each reference pattern image so as to store information on the reference pattern image in the RAM  150   b.    
   The control unit  150  performs above operations, for example, conversion of the image density into the toner adhesion amount, on the reference image patches Pk 1 , Pc 1 , Pm 1 , and Py 1  in sequence. The development potential of each reference pattern image and the toner adhesion amount obtained by the control unit  150  is shown in  FIG. 6 . 
   Referring to  FIG. 6 , a relationship between the development potential of each reference pattern image and the toner adhesion amount is plotted. An X-axis shows the development potential that is a difference between a development bias V B  and a reference pattern image potential V D , V B -V D  (V). A Y-axis shows the toner adhesion amount per unit area (mg/cm 2 ). The control unit  150  selects a linear region of the relationship between the development potential of the reference pattern image and the toner adhesion amount based on plotted data in  FIG. 6 , and applies a least squares method with respect to data within the linear region. Thereby, the control unit  150  calculates a straight line equation A obtained by a linear approximation of the relationship between the development potential of the reference pattern image and the toner adhesion amount for each color. By using the straight line equation A, the control unit  150  calculates the development potential for obtaining a target toner adhesion amount, and attempts to maintain the image density by feeding back to the image condition of the reference pattern image. 
   Referring to  FIG. 8 , since the P sensors  56 Y,  56 M,  56 C, and  56 K are configured to be the same except for the toner colors, one of the P sensors  56 Y,  56 M,  56 C, and  56 K is illustrated as an example P sensor  56 . The color symbols Y, M, C, and K indicating yellow, magenta, cyan, and black are omitted as necessary. As shown in  FIG. 8 , the P sensor  56  includes an oscillator  21 , a resonance circuit  22 , a phase comparison circuit  23 , an integrating circuit  24  and an impedance exchange circuit  25 . 
   The oscillator  21  includes a resonator OS of a solid matter, for example, a crystal and a ceramic, a capacitor C 1 , a capacitor C 2 , an exclusive OR circuit EOR 1 , and resistances R 1  and R 2 . The oscillator  21  oscillates at an oscillation frequency which is determined by a property of a vibration frequency of the solid resonator OS. 
   The resonance circuit  22  includes a first LC resonance circuit, a second LC resonance circuit, a resistance R 3 , and a resistance R 8 . The first LC resonance circuit includes a coil L 1 , a capacitor C 3 , and a variable-capacitance diode D. The second LC resonance circuit includes a coil L 2 , and a capacitor C 4 . The coils L 1  and L 2  are coupled by a magnetic coupling constant k. 
   The oscillation frequency of the oscillator  21  is close to resonance frequencies of the first and second LC resonance circuits in the resonance circuit  22 , and the coils L 1  and L 2  have inductances which may be varied by the permeability of the developer  53  in the development device  5 . In the variable-capacitance diode D, a control voltage as an external input voltage Vcnt from the control unit  150  is applied across both terminals through the resistance R 8 , and a capacitance is varied depending on the external input voltage Vcnt. The resonance circuit  22  receives an output from the oscillator  21 , and an output from the resonance circuit  22  is varied by a difference between the oscillation frequency of the oscillator  21  and the resonance frequency of the resonance circuit  22 . The resonance frequency of the resonance circuit  22  is varied by the permeability of the developer  53  in the development device  5 , and the permeability of the developer  53  is detected by varying the output of the resonance circuit  22 . 
   The phase comparison circuit  23  includes an exclusive OR circuit EOR 2 , a capacitor C 5 , a resistance R 4 , and a resistance R 5 . The phase comparison circuit  23  detects a phase difference by comparing an output phase of the oscillator  21  and an output phase of the resonance circuit  22 . As shown in  FIG. 8 , the exclusive OR circuit EOR 1  outputs an output V 1  which is input to one of input areas of the exclusive OR circuit EOR 2 . The capacitor C 5 , the resistance R 4 , and the resistance R 5  are connected so as to input an output V 2  to another input area of the exclusive OR circuit EOR 2 . 
   The integrating circuit  24  includes a resistance R 6 , and a capacitor C 6 . The integrating circuit  24  integrates an output value of the phase comparison circuit  23 . The impedance exchange circuit  25  includes a transistor Q and a resistance R 7 . The impedance exchange circuit  25  performs an impedance exchange. An output value from the integrating circuit  24  as a toner density detection signal in corresponding to a variation of the permeability of the developer  53  in the development device  5  is output to the control unit  150  through the impedance exchange circuit  25 . 
   In the image forming apparatus of the present invention, when a new process cartridge, for example  6 Y, is installed, the P sensor, for example  56 Y, is read. Each of the development devices  5 Y,  5 M,  5 C, and  5 K in the respective new process cartridges  6 Y,  6 M,  6 C, and  6 K is filled with a developer having the toner density of 8 wt %. The control unit  150  reads the P sensor  56  by sequentially varying the external input voltage Vcnt of the P sensor  56  such that an output value Vt of the P sensor  56  becomes 2.5V with respect to the developer with the toner density of 8 wt %. The control unit  150  stores the external input voltage Vcnt of the P sensor  56  obtained during reading for a color basis. When the permeability of the developer  53  in the development device  5  is detected by the P sensor  56 , the Vcnt for respective color stored in the RAM  150   b  is set to the P sensor  56 , for example, by applying to the variable-capacitance diodes D of the P sensor  56 . 
   When the transfer sheet is fed in a normal printing operation, the permeability of the developer  53  in the development device  5  during the sheet feeding is detected by the P sensor  56 . The control unit  150  compares a target value Vref of the P sensor  56  and the output value Vt of the P sensor  56  so as to control the toner supply quantity to the development device  5  from the toner supply device based on a difference of the comparison. Specifically, the control unit  150  determines the toner supply quantity of each toner supply device depending on whether or not to satisfy an expression (Vt−Vref)&gt;Vref by using Formulas 1 and 2 stated later. During a next image forming in the printing operation, the control unit  150  drives the toner supply motors  41  (shown in  FIG. 2 ) to be rotationally driven so that the toner supply device supply the toner with the determined toner supply quantity to the development devices  5  by the toner supply motors  41  (see FIG.  2 ).
 
 Ts =α×( Vt−V ref)/ Sp,   Formula 1:
 
where Ts represents the toner supply quantity, α represents a proportionality coefficient, and Sp represents the P sensor sensitivity. Formula 1 is satisfied when the output value Vt is greater than the target value Vref.
 
Ts=0,  Formula 2:
 
where Ts represents the toner supply quantity. Formula 2 is satisfied when the output value Vt is equal to or smaller than the target value Vref.
 
   Here, the control unit  150  measures the output value Vt of the P sensor  56  with respect to the permeability of the developer  53  in the development device  5 , and updates the value Vref stored in the control  150  based on the measured output value Vt. In Formula 1, α is the proportionality coefficient which determines a response of the toner supply quantity with respect to the output value of the P sensor  56 . In this exemplary embodiment, α=0.3. 
   Referring to  FIG. 5 , a relationship between the output value of the P sensor  56  and the toner density in a process linear velocity is illustrated. As shown in  FIG. 5 , when a normal process linear velocity of 155 mm/sec and a half of the normal process linear velocity of 77.5 mm/sec are compared, there is a tendency that a slower process linear velocity has a higher Vt value with respect to the same toner density. Hereafter, a difference of the output value Vt of the P sensor  56  with respect to a difference of the process linear velocity is referred to as a Vt shift amount. When the output value Vt of the P sensor  56  with respect to the permeability of the developer  53  in the development device  5  at half of the normal process velocity is substituted into the formula 1, the toner supply quantity becomes excessive because of the Vt shift amount. Consequently, when the transfer sheet is fed at half of the normal process linear velocity, a Formula 3 stated below is expressed in which a HalfVt is the output value of the P sensor at half of the normal process linear velocity, Vt is the output value of the P sensor  56  at the normal process, and VtS is the Vt shift amount.
 
 Vt =Half Vt−VtS   Formula 3:
 
The control unit  150  converts the half velocity HalfVt of the P sensor into the Vt at the normal process velocity by Formula 3, and estimates an output variation of the P sensor  56  by the external input voltage Vcnt so as to determine the toner supply quantity according to Formulas 1 and 2. However, the Vt shift amount may vary depending on the P sensor  56 , for example, P sensors A and B as shown in  FIG. 5 . This variation of the Vt shift amount may cause the toner supply quantity during the sheet feeding at the half of the normal velocity to deviate from a target toner supply quantity, and the toner density may not be stabilized. Thereby, the control unit  150  calculates the Vt shift amount by the Vcnt value at which the P sensor  56  is read so as to correct the variation of the Vt shift amount.
 
   Referring to  FIG. 7 , a relationship between the Vcnt value at which the P sensor is read and the Vt shift amount at which the process linear velocity is switched is graphed. As shown in  FIG. 7 , the Vct value and Vt shift amount have a correlation, and are approximated at a quadratic curve. The Vt shift amount is a difference between a Vt value before the process linear velocity is switched and a Vt value after the process linear velocity is switched. The control unit  150  calculates the Vt shift amount with respect to the Vcnt value by utilizing the correlation to store in the memory in the image forming apparatus so that the Vt shift amount is used for calculating the Vt of Formula 3. Specifically, the control unit  150  calculates the Vt shift amount by a Formula 4 stated below to store in the memory in the image forming apparatus so that the Vt shift amount is used for calculating the Vt of Formula 3.
 
 VtS=− 0.3728×( Vcnt ) 2 +2.6397×( Vcnt )−3.6733,  Formula 4:
 
where VtS represents the Vt shift amount, and Vcnt represents the external input voltage.
 
   The variation of the Vt shift amount with a maximal range of 0.5V may be decreased to ±0.1V by calculating Formula 4 as shown in  FIG. 7 . Thereby, the toner supply quantity at which the process linear velocity is switched may be controlled with a higher accuracy. 
   According to the exemplary embodiment of the present invention, the external input voltage Vcnt by which the output variation from the resonance circuit  22  of the P sensor  56  is adjusted is stored, and the Vt shift amount of the P sensor  56  at which the process linear velocity is switched in the same toner density is estimated based on the stored external input voltage. Thereby, the output value Vt of the P sensor at which the process linear velocity is switched is corrected by the Vt shift amount so that the toner supply quantity at which the process linear velocity is switched may be accurately controlled. 
   According to the exemplary embodiment of the present invention, the output variation from the resonance circuit  22  of the P sensor  56  is adjusted by the external input voltage Vcnt with the developer having a given toner density so that the P sensor is read by a certain condition. Thereby, the output variation of the P sensor may be estimated by the external input voltage Vcnt so that the Vt shift amount of the P sensor at which the process linear velocity is switched is accurately predicted. 
   According to the exemplary embodiment of the present invention, the Vt shift amount of the P sensor at which the process linear velocity is switched is calculated by a quadratic approximation formula with employing the external input voltage Vcnt by which the output variation from the resonance circuit  22  of the P sensor is adjusted. Thereby, the Vt shift amount of the P sensor at which the process linear velocity is switched may be accurately estimated. 
   Numerous additional modifications and variations are possible in light of the above teachings. It is therefore to be understood that within the scope of the appended claims, the disclosure of this patent specification may be practiced otherwise than as specifically described herein.