Patent Publication Number: US-7720402-B2

Title: Method and apparatus for image forming capable of controlling toner concentration accurately

Description:
This patent specification is based on Japanese patent application, No. 2006-078867 filed on Mar. 22, 2006 in the Japan Patent Office, the entire contents of which are incorporated by reference herein. 
   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to a method and apparatus for image forming, and more particularly to a method and apparatus for image forming capable of controlling toner-concentration accurately. 
   2. Discussion of the Background 
   An image forming apparatus that employs an electrophotographic method has been developed rapidly. Such an apparatus includes a printer, a copier, a facsimile machine, and a multi-function system, for example. 
   Recently, there is increasing demand that such an image forming apparatus have high stability and durability in addition to a high performance to obtain high quality images. Namely, it is requested that the image forming apparatus can maintain a constant quality of image forming that is less affected by environmental variation. 
   A background image forming apparatus commonly employs a two-component developer method using a two-component developer to visualize an image in an image forming operation because the two-component developer easily handles color images. The two-component developer (developer) includes non-magnetic toner and magnetic carrier. 
   In the two-component developer method, the background image forming apparatus holds the two-component developer on a developing sleeve which is a developer carrier. The background image forming apparatus forms a magnetic brush generated by magnetic poles provided in the developing sleeve. The two-component developer is conveyed to a developing region between the developing sleeve and a photoreceptor in accordance with a rotation of the developing sleeve. While the developer is conveyed to the developing region, a plurality of magnetic carriers in the developer are gathering together along a magnetic field generated by the magnetic poles to form the magnetic brush. 
   It is important to control a weight ratio of the toner and the carrier accurately to improve stability of the two-component developer. If toner-concentration is too high, scumming of the image may occur. As a result, resolution of a fine image may be decreased. Meanwhile, if toner-concentration is too low, another problems may occur. For example, low concentration may occur in a plain image area, or carrier adhesion may be generated. 
   To solve these problems, the toner-concentration of the developer needs to be adjusted to a necessary range by controlling the toner supply amount to the developer being used. Therefore, a sensor may be employed to detect the toner-concentration and to compare an output voltage of the sensor with a reference value of the toner-concentration. The toner supply amount is then determined based on the comparison result. 
   There are a variety of methods to detect toner-concentration. One method is to use a permeability sensor. A permeability of the developer changes when the toner-concentration of the developer is changed. The permeability sensor detects and compares a detected value with a reference value to determine if the toner supply amount needs to be adjusted. 
   Another method is to use a light sensor. In this method, a reference image pattern is formed on a photoreceptor, or an intermediate transfer belt initially. The light sensor detects light reflections from an image area having an actual image and a background area having no image. The toner-concentration of the developer is detected based on the detection result. 
   Further, the reference image pattern is transferred to paper from the photoreceptor or intermediate transfer belt during image forming process. The light sensor detects the light reflections from the image area and the background area on the paper. Then, a reference value Vref is controlled. However, in this method, toner is wasted because of the actual image forming on the photoreceptor, or the intermediate transfer belt, or during the transfer process to the paper. 
   In another background image forming apparatus, a controller detects toner-concentration of the developing unit and compares a detected value with a threshold value. The controller controls the toner-concentration of the developing unit by changing the threshold value by a predetermined value in accordance with a change of a linear velocity of a photoreceptor. 
   However, when the linear velocity of a photoreceptor is large, an output signal of the permeability sensor may be saturated. As a result, the toner-concentration can not be detected in the saturated region. 
   SUMMARY OF THE INVENTION 
   This patent specification describes a novel toner-concentration controller including a controller configured to control a toner supply amount in accordance with a detection result of a toner-concentration of two-component toner, and a sensor unit configured to detect the toner-concentration of two-component toner. The sensor unit includes a correction mechanism configured to correct an output signal of the sensor unit by changing an external-input voltage, based on relationship data between an output voltage change of the sensor unit of a toner-concentration of unused developer, to control the toner supply amount when the toner-concentration of the two-component toner deviates a predetermined amount from the toner-concentration of the unused developer. The sensor unit is configured to detect the toner-concentration of the unused developer from unused two-component toner based on a change in the external-input voltage. 
   Further, this patent specification describes a novel toner-concentration controller including a sensor unit which is a permeability sensor and including a resonant circuit and an oscillator. The resonant circuit includes a coil configured to change an inductance in accordance with a permeability of the two-component toner, and an adjusting mechanism configured to adjust an output of the resonant circuit by the external-input voltage when a change of the toner-concentration of the two-component toner is detected by an inductance change of the coil. The oscillator is configured to oscillate around a resonance frequency of the resonant circuit. 
   Further, this patent specification describes a novel method of controlling a toner-concentration, including the steps of detecting a toner-concentration of unused two-component toner with a sensor unit based on a change in an external-input voltage, detecting a toner-concentration of two-component toner during printing, supplying developer in accordance with an output signal of the sensor unit, and correcting an output signal of the sensor unit by changing the external-input voltage, based on relationship data between an output voltage change of the sensor unit and a the toner-concentration of unused developer, to control a toner supply amount when the toner-concentration of the two-component toner deviates a predetermined amount from the toner-concentration of the unused developer. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     A more complete appreciation of the disclosure 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 printer as one exemplary embodiment of an image forming apparatus according to present disclosure; 
       FIG. 2  is a relevant part of a toner image forming unit of the printer; 
       FIG. 3  is a block diagram showing a relevant part of an electric circuit of the printer; 
       FIG. 4  is a schematic diagram of an intermediate transfer belt showing each color reference pattern; 
       FIG. 5  is a plot of a relationship between a developing potential of each reference pattern image and a toner adhesive amount; 
       FIG. 6  is a circuit configuration of a toner concentration sensor (T-sensor); 
       FIG. 7  is a graph representing a relationship between a toner-concentration and an output voltage of the T-sensor at a large change of the toner-concentration; 
       FIG. 8  is a plot of a relationship between an external-input voltage and an output voltage of the T-sensor; 
       FIG. 9  is a graph representing a relationship between a toner-concentration and an output voltage of the T-sensor when a process linear velocity is changed; 
       FIG. 10  is a graph representing a relationship between a toner-concentration and an output voltage of the T-sensor at each condition of temperature and humidity; and 
       FIG. 11  is a graph representing a relationship between a toner-concentration and an output voltage of the T-sensor at each image area ratio. 
   

   DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
   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, particularly to  FIG. 3 , a toner-concentration controller according to an exemplary embodiment of the present invention is described. 
     FIG. 1  illustrates a first exemplary embodiment of a printer as one example of an image forming apparatus using electrophotography according to the present disclosure. A basic configuration of the printer will now be described. 
   Each image forming unit  6 Y,  6 M,  6 C, and  6 K forms a yellow (Y), magenta (M), cyan (C), and black (K) image respectively. Further, each toner image forming unit  6 Y,  6 M,  6 C, and  6 K is provided in a form of process cartridge which is detachably attached to the main body of the printer  100 . 
   The four image forming units  6 Y,  6 M,  6 C, and  6 K (the process cartridges) have a same configuration, but handle different toner colors, yellow (Y), magenta (M), cyan (C), and black (K) as image forming materials. The process cartridges  6 Y,  6 M,  6 C, and  6 K may be exchanged before an end of their lifetime. 
     FIG. 2  illustrates the process cartridge  6 Y for forming a yellow color toner image. As shown in  FIG. 2 , the process cartridge  6 Y includes a photosensitive drum  1 Y, a drum cleaning unit  2 Y, a diselectrifier (not shown), a charging unit  4 Y, and a developing unit  5 Y. The above components are integrated in the process cartridge  6 Y. 
   A permeability sensor  56 Y (T-sensor) is provided underneath of the developing unit  5 Y as a toner-concentration sensor which detects a toner-concentration in the developing unit  5 Y. The process cartridge  6 Y is detachably attached to the main body of the printer  100  and may be exchanged as a consumable part. 
   The charging unit  4 Y charges uniformly a surface of the photosensitive drum  1 Y which is rotated in a clockwise direction by a drive mechanism (not shown). A laser beam L emitted from a light-writing unit  7  (shown in  FIG. 1 ), which is an exposure unit, is exposed and is scanned on the uniformly charged surface of the photosensitive drum  1 Y in accordance with yellow image information. As a result, an electrostatic latent image of a yellow color is formed on the surface of the photosensitive drum  1 Y. The electrostatic latent image of the yellow color is developed with a two-component developer which includes non-magnetic yellow toner and magnetic carrier. 
   A transfer bias potential is applied from a high voltage source (not shown) to a first transfer bias roller  9 Y, which is a transfer mechanism, so as to form a transfer electric field. The toner image on the surface of the photosensitive drum  1 Y is transferred onto an intermediate transfer belt  8  by the transfer electric field at a transfer position between the photosensitive drum  1 Y and the intermediate transfer belt  8 . 
   The drum cleaning unit  2 Y removes residual toner on the surface of the photosensitive drum  1 Y at a predetermined position after the surface of the photosensitive drum  1 Y passes through the transfer position. The diselectrifier (not shown) diselectrifies the residual charge on the surface of the photosensitive drum  1 Y after cleaning. By removing the electricity, the surface of the photosensitive drum  1 Y is initialized to prepare for the next image forming process. 
   The developing unit  5 Y forms a magnetic brush by magnetic poles provided in a developer sleeve  51 Y by agitating and conveying the two-component developer  53 Y stored in a developer storage  54 Y by an agitating-conveyance member  55 Y. The developer sleeve  51 Y works as a developer carrier. The agitating-conveyance member  55 Y and the developer sleeve  51 Y are driven to be rotated by a rotation-drive mechanism (not shown). 
   When a process linear velocity is changed, linear velocities of the agitating-conveyance member  55 Y and the developer sleeve  51 Y are changed by the rotation-drive mechanism. The two-component developer  53 Y on the developer sleeve  51 Y is conveyed to a development region in accordance with the rotation of the developer sleeve  51 Y. 
   A plurality of magnetic carriers in the two-component developer  53 Y are gathering together along the magnetic field line formed by the magnetic poles provided in the developer sleeve  51 Y. As a result, the magnetic carriers form the magnetic brush. 
   A thickness of the two-component developer  53 Y on the developer sleeve  51 Y is regulated by a regulatory member  52 Y. A developing bias potential is applied from the high voltage source to the developer sleeve  51 Y at a position where the developer sleeve  51 Y faces the photosensitive drum  1 Y. The toner in the developer attaches on the electrostatic latent image. Thus, the electrostatic latent image is developed. 
   The toner is supplied into the developer storage  54 Y of the developing unit  5 Y from a toner supply unit  32 Y. The toner supply unit  32 Y (see  FIG. 1 ) is driven by a drive motor  41 Y so as to supply toner into the developer storage  54 Y. 
   Referring again to  FIG. 1 , similarly to the developing unit  5 Y of the process cartridges  6 Y, each developing unit  5 M,  5 C, and  5 K of the other process cartridges  6 M,  6 C, and  6 K forms a magnetic brush by magnetic poles provided in the developer sleeves by agitating and conveying the two-component developer by agitating-conveyance members. The agitating-conveyance members and the developer sleeves are driven to be rotated by a rotation-drive mechanism (not shown). 
   When a process linear velocity is changed, linear velocities of the agitating-conveyance member and the developer sleeve are changed by the rotation-drive mechanism. The two-component developer on the developer sleeve is conveyed to a development region in accordance with the rotation of the developer sleeve. A plurality of magnetic carriers in the two-component developer are gathering together along the magnetic field line formed by the magnetic poles provided in the developer sleeve. As a result, the magnetic carrier forms the magnetic brush. 
   A thickness of the two-component developer on the developer sleeve is regulated by a regulatory member. A developing bias potential is applied from the high voltage source to the developer sleeve at a position where the developer sleeve faces the photosensitive drums  1 M,  1 C, and  1 K. The toner in the developer attaches on the electrostatic latent image. Thus, the electrostatic latent image is developed. 
   Each color toner M, C, and K is supplied into the developer storage of developing units  5 M,  5 C, and  5 K from toner supply units  32 M,  32 C, and  32 K. The toner supply units  32 M,  32 C, and  32 K are driven by drive motors  41 M,  41 C, and  41 K to supply toner into the developer storage of the developing units  5 M,  5 C, and  5 K. 
   As shown in  FIG. 1 , similar to the process cartridges  6 Y, the process cartridges  6 M,  6 C, and  6 K include photosensitive drums  1 M,  1 C, and  1 K, drum cleaning units, diselectrifiers, charging units and developing units  5 M,  5 C, and  5 K. Each toner image M, C, and K is formed on the photosensitive drums  1 M,  1 C, and  1 K. Each color toner image is transferred onto the intermediate transfer belt  8  by being superimposed on the yellow toner image Y by the first transfer bias rollers  9 M,  9 C, and  9 K which work as transfer mechanisms. 
   Underneath of the process cartridges  6 Y,  6 M,  6 C, and  6 K, the exposure unit  7  is provided as an electrostatic latent image forming unit. The exposure unit  7  emits each laser beam L from a plurality of light sources in accordance with each color image information. Each laser beam L is irradiated onto the photosensitive drums  1 Y,  1 M,  1 C, and  1 K, and exposes the surface of the photosensitive drums  1 Y,  1 M,  1 C, and  1 K. 
   The exposure unit  7  scans the laser beam L using a polygon mirror which is driven to be rotated by a motor and irradiates the laser beam L onto photosensitive drums  1 Y,  1 M,  1 C, and  1 K through a plurality of optical lenses and mirrors. Each electrostatic latent image is formed on the photosensitive drums  1 Y,  1 M,  1 C, and  1 K respectively. 
   Underneath of the exposure unit  7 , a paper feed mechanism is provided. The paper feed mechanism includes a paper storage cassette  26  and a paper feed roller  27 . The paper storage stores paper P by piling a plurality of the papers. The paper P is a recording medium to form the image thereon. The paper feed roller  27  contacts a top of the paper P. When the paper feed roller  27  is rotated in a counterclockwise direction by a drive mechanism (not shown), a paper P on top of the piled papers in the paper storage cassette  26  is fed by the paper feed roller  27  towards resist roller pair  28 . 
   The resist roller pair  28  rotate to clip the paper P. Soon after clipping the paper P, the resist roller pair  28  stops to rotate temporarily. The resist roller pair  28  feeds the paper P towards a secondary transfer nip at a predetermined timing. 
   At an upper part of the process cartridges  6 Y,  6 M,  6 C, and  6 K, an intermediate transfer unit  15  is provided as an intermediate transfer mechanism which works as an image carrier. The intermediate transfer unit  15  includes an endless intermediate transfer belt  8  which is extended among a plurality of rollers and carries the image. The intermediate transfer unit  15  further includes four first transfer bias rollers  9 Y,  9 M,  9 C, and  9 K, a cleaning unit  10 , a secondary transfer backup roller  12 , a cleaning backup roller  13 , and a tension roller  14  in addition to the intermediate transfer belt  8 . 
   Further, the intermediate transfer belt  8  is extended among the secondary transfer backup roller  12 , the cleaning backup roller  13 , and the tension roller  14 . The intermediate transfer belt  8  is moved by a rotation of at least one roller in a counterclockwise direction. 
   Each first transfer bias roller  9 Y,  9 M,  9 C, and  9 K forms a first transfer nip with the photosensitive drum  1 Y,  1 M,  1 C, and  1 K by clipping the intermediate transfer belt  8 . A transfer bias potential which is opposite to the potential of the toner, for example, a plus voltage, is applied from the high voltage source to the inner surface of the intermediate transfer belt  8  through the first transfer bias rollers  9 Y,  9 M,  9 C, and  9 K. The secondary transfer backup roller  12 , the cleaning backup roller  13 , and the tension roller  14  are grounded. 
   While the intermediate transfer belt  8  is moving and is passing the first transfer nip for each color Y, M, C, and K serially, each toner image on the photosensitive drums  1 Y,  1 M,  1 C, and  1 K is transferred by superimposing one toner image after another. As a result, a superimposed four color toner image (full color image) is formed on the intermediate transfer belt  8 . 
   The secondary transfer backup roller  12  forms a secondary transfer nip with the secondary transfer roller  19  by clipping the intermediate transfer belt  8 . A transfer bias potential is applied from the high voltage source to the secondary transfer roller  19 . The four color toner image formed on the intermediate transfer belt  8  is transferred onto the paper P fed from the resist roller pair  28  at the secondary transfer nip. 
   Residual toner, which is not transferred to the paper P, is adhered on a portion of the intermediate transfer belt  8  that has passed through the secondary transfer nip. The residual toner is removed by the cleaning unit  10 . 
   At the secondary transfer nip, the paper P is clipped by the intermediate transfer belt  8  and the secondary transfer roller  19  and is conveyed to the opposite direction of the resist roller pair  28 . The intermediate transfer belt  8  and the secondary transfer roller  19  move in the same direction at each surface contacting each other. The paper P fed from the secondary transfer nip passes through a fixing unit  20 . While passing through the fixing unit  20 , the four color toner image is fixed by heat and pressure. 
   The paper P is output to outside of the printer  100  through a paper-output roller pair  29 . A stack unit  30  is provided at an upper part of the printer  100 . The papers P are stacked one after another in the stack unit  30 . 
   A reflective photo sensor  40  is provided at upper part of the secondary transfer backup roller  12  and works as an image-concentration-detecting mechanism. The reflective photo sensor  40  outputs a signal in accordance with a light reflection coefficient on the intermediate transfer belt  8 . 
   As the reflective photo sensor  40 , a diffusive light detection type sensor, or a specular-reflectance light detection type sensor, for example, may be selected depending on a condition to utilize a difference between a light reflective amount on the surface of the intermediate transfer belt  8  and a reference light reflective amount of a reference pattern. Operation of the reflective photo sensor  40  will be described later. 
     FIG. 3  illustrates a block diagram showing a relevant part of an electric circuit of the printer  100 . The printer  100  includes a controller  150  as shown in  FIG. 3 . The controller  150  controls toner image forming units  6 Y,  6 M,  6 C, and  6 K, a light-writing unit  7 , the paper feed cassette  26 , a rotation drive unit of the resist roller pair  28 , the intermediate transfer unit  15 , the reflective photo sensor  40 , T-sensors  56  ( 56 Y,  56 M,  56 C, and  56 K) of the process cartridges  6 Y,  6 M,  6 C, and  6 K. Further, the controller  150  includes CPU (central processing unit)  150   a  and RAM (random access memory)  150   b . The CPU  150   a  controls a computing unit (not shown) and the RAM  150   b  stores data. 
   The controller  150  examines image forming performances of the toner image forming units  6 Y,  6 M,  6 C, and  6 K at predetermined timings, for example, at an input of a main power (not shown), at a waiting time after a predetermined time from the main power input, and at a waiting time after a predetermined repetition of image forming operations. The controller  150  controls toner supply amounts, from each color toner supply unit  32 Y,  32 M,  32 C, and  32 K, to the developing unit  5 Y,  5 M,  5 C, and  5 K respectively. 
   More specifically, the controller  150  performs correction of the reflective photo sensor  40  at a predetermined time. At a correction process of the reflective photo sensor  40 , the controller  150  searches an emitting light amount of the reflective photo sensor  40  to fit a detection voltage with a voltage 4.0v+−0.2v by changing the emitting light amount of the reflective photo sensor  40  sequentially. The emitting light amount obtained at the search process is used at a detection of a toner adhesive amount on the reference pattern. 
   Then, the controller  150  causes the charging units  4 Y,  4 M,  4 C, and  4 K to charge the photosensitive drums  1 Y,  1 M,  1 C, and  1 K uniformly by rotating the photosensitive drums  1 Y,  1 M,  1 C, and  1 K. The controller  150  causes the high voltage source to increase a charge-up voltage gradually applied to the photosensitive drums  1 Y,  1 M,  1 C, and  1 K. This procedure is different from a uniform charging process performed in a normal printing process. The charging voltage in the normal printing process may be, for example, −700v. 
   The controller  150  causes the light-writing unit  7  to form an electrostatic latent image of the reference image on the photosensitive drums  1 Y,  1 M,  1 C, and  1 K by scanning the laser beam. The electrostatic latent image is then developed on the toner image forming units  6 Y,  6 M,  6 C, and  6 K. Each color reference pattern image is formed on the photosensitive drums  1 Y,  1 M,  1 C, and  1 K respectively in this development process. 
   During the development process, the controller  150  causes the high voltage source to increase a developing bias voltage gradually applied to the toner image forming units  6 Y,  6 M,  6 C, and  6 K. As a result, a reference pattern image having a light concentration is formed on the photosensitive drums  1 Y,  1 M,  1 C, and  1 K at first. Then, reference pattern images having a darker concentration are being formed progressively. The pattern image forming process will be described in detail hereinafter. 
   On the contrary, if the charge-up and developing bias voltages for the photosensitive drums  1 Y,  1 M,  1 C, and  1 K are decreased gradually, a reference pattern image having a dark concentration is formed at first and reference pattern images having a lighter concentration are being formed progressively. 
   In general, it takes longer to decrease an output voltage of the high voltage source. Therefore, it may take longer to form the reference pattern if the output voltage of the high voltage source is decreased. Each color reference pattern image on the photosensitive drums  1 Y,  1 M,  1 C, and  1 K is formed on the intermediate transfer belt  8  to not overlap each other. 
   When each color reference pattern image passes through a point which faces the reflective photo sensor  40  in accordance with the movement of the intermediate transfer belt  8 , each color reference pattern image is detected by the reflective photo sensor  40 . The reflective photo sensor  40  generates a detection signal and sends the detection signal to the controller  150 . The controller  150  calculates a light reflection coefficient of each reference image based on the detection signal sent from the reflective photo sensor  40 . 
   The light reflection coefficient is stored in the RAM  150   b  as concentration pattern data. The reference pattern image formed on the intermediate transfer belt  8  is removed by the cleaning unit  10  after the reference pattern image passes through a point where the reflective photo sensor  40  faces the intermediate transfer belt  8 . 
     FIG. 4  illustrates a schematic diagram of the intermediate transfer belt  8  showing a part of color reference patterns P (Py, Pm, Pc, and Pk). The reference pattern image Py is a yellow color pattern, the reference pattern image Pm is a magenta color pattern, the reference pattern image Pc is a cyan color pattern, and the reference pattern image Pk is a black color pattern. In  FIG. 4 , two reference pattern images Pk and Pc are shown. Each color pattern image includes ten reference image components (Pk 1 , Pk 2 , . . . , Pk 9 , Pk 10 , and Pc 1 , Pc 2 , . . . , Pc 9 , Pc 10 ), which line up with a distance of 13 mm between each image component. The reference image components (Pm 1  to Pm 10 , Py 1  to Py 10 ) will follow the reference image components (Pc 1  to Pc 10 ). 
   In the printer  100 , each reference image component has a rectangular shape with a vertical size of 13 mm and a horizontal size of 5 mm. A length L 2  of each reference pattern image Py, Pm, Pc, and Pk is 247 mm (L 2 =247 mm). The reference pattern images Py, Pm, Pc, and Pk are formed on the intermediate transfer belt  8  at different timings to not overlap each other. Thus, the image formation of the reference pattern image is different from the toner image formation at a normal printing process. 
   The reflective photo sensor  40  is provided above the intermediate transfer belt  8  at the upper right of  FIG. 4 . After the detection process of the reference pattern image, the reference pattern image is removed by the cleaning unit  10  of the intermediate transfer unit  15 , referring to  FIGS. 1 and 4 . 
   The reflective photo sensor  40  detects the light reflections from each reference image component of the reference pattern image Py, Pm, Pc, and Pk in the following order. 
   The reflective photo sensor  40  detects the ten reference image components of the reference pattern image Pc after the detection of the ten reference image components of the reference pattern image Pk. Then, the reflective photo sensor  40  detects ten reference image components of the reference pattern image Pm and Py one after another. The reflective photo sensor  40  generates and outputs a voltage signal to the controller  150  in accordance with the light reflection of each reference pattern image. The controller  150  calculates image concentration of each reference image component based on the voltage signal sent from the reflective photo sensor  40 . Calculated data is stored in the RAM  150   b  one after another. 
   The controller  150  converts the image concentration of each reference image component to a toner adhesive amount in a following way. The controller  150  converts the output signal corresponding to each ten reference image components of the reference pattern image Py, Pm, Pc, and Pk to the toner adhesive amount based on the relationship between the toner adhesive amount and the detected voltage signal as shown in  FIG. 5 . Then, converted data is stored in the RAM  150   b . While storing the converted data in the RAM  150   b , the controller  150  estimates a developing potential from a condition of each reference pattern image. Information data of the reference pattern image is also stored in the RAM  150   b . The process steps described above are performed on the reference pattern images Pk 1 , Pc 1 , Pm 1 , and Py 1  one after another. 
     FIG. 5  is an X-Y plot of the relationship between a developing potential of each reference pattern image and a toner adhesive amount obtained by the process steps. In  FIG. 5 , potential (potential difference VB-VD between the developing potential VB and reference pattern image potential VD) (V) is shown on the X-axis and the toner adhesive amount M/A (mg/cm 2 ) is shown on the Y-axis. 
   The controller  150  selects a linear portion of the plotted data which represents the relationship between the developing potential of each reference pattern image and the toner adhesive amount. The controller  150  calculates a linear equation (Y=A 1 ×X+B 1 ) for each color by applying the least-squares method to the plotted data in the linear portion. Further, the controller  150  calculates a developing potential to obtain a target toner adhesive amount by the linear equation. The calculated developing potential is fed back to image forming condition. Namely, the image forming condition is controlled by the developing potential. As a result, the image concentration can be kept to a predetermined level by the feed back process. 
     FIG. 6  illustrates a circuit configuration of the T-sensor  56  ( 56 Y,  56 M,  56 C, and  56 K). The T-sensor  56  includes an oscillator  21 , a resonance circuit  22 , a phase comparator circuit  23 , an integration circuit  24 , and an impedance converting circuit  25 . The oscillator  21  includes a resonator OS, capacitors C 1  and C 2 , an exclusive OR-circuit EOR 1 , and resistors R 1  and R 2 . The resonator OS includes solid resonator, for example, crystal resonator or ceramic resonator. The oscillator  21  oscillates with a natural frequency of the solid resonator. 
   The resonance circuit  22  includes first and second LC resonance circuits, and resistors R 3  and R 8 . The first LC resonance circuit includes a coil L 1 , capacitor C 3 , and a variable capacitance diode D. The second LC resonance circuit includes a coil L 2  and capacitor C 4 . The coils L 1  and L 2  are coupled with a magnetic-coupling-coefficient constant k. 
   The oscillation frequency of the oscillator  21  is close to the resonance frequency of the first and second LC resonance circuits. Inductances of the coils L 1  and L 2  change in accordance with permeability (toner-concentration) of developer  53  ( 53 Y,  53 M,  53 C, and  53 K) in developing unit  5 . A control voltage is applied as an external voltage Vcnt to both ends of the variable capacitance diode D from the controller  150  through resistor R 8 . 
   The resonance circuit  22  receives an output signal of the oscillator  21  and changes an output of the resonance circuit  22  in accordance with a difference between the oscillation frequency of the oscillator  21  and the resonance frequency of the resonance circuit  22 . The permeability (toner-concentration) of developer  53  ( 53 Y,  53 M,  53 C, and  53 K) is detected by the output change of the resonance circuit  22  because the permeability (toner-concentration) of developer  53  ( 53 Y,  53 M,  53 C, and  53 K) in developing unit  5  affects the resonance frequency of the resonance circuit  22 . 
   The phase comparator circuit  23  includes an exclusive OR-circuit EOR 2 , capacitor C 5 , and resistors R 4  and R 5 . The exclusive OR-circuit EOR 2  has a first voltage V 1 , from the oscillator  21 , and a second voltage V 2 , from the resonance circuit  22 , as inputs. The phase comparator circuit  23  compares a phase of the oscillator  21  with a phase of the resonance circuit  22  and detects a phase difference between them. The integration circuit  24  includes a resistor R 6  and a capacitor C 6  to integrate an output of the phase comparator circuit  23 . 
   The impedance converting circuit  25  includes a transistor Q and a resistor R 7  to perform impedance conversion. The output signal of the integration circuit  24  is output to the controller  150  as a toner-concentration detection signal through the impedance converting circuit  25 . The toner-concentration detection signal is a corresponding signal to the change of the permeability (toner-concentration) of developer  53  ( 53 Y,  53 M,  53 C, and  53 K) in developing unit  5 . 
   In the printer  100 , when brand new process cartridges  6 Y,  6 M,  6 C and  6 K are installed, the controller  150  performs correction of the T-sensors  56 Y,  56 M,  56 C and  56 K of the process cartridges  6 Y,  6 M,  6 C and  6 K under a constant toner-concentration using unused two-component developer. The developing unit  5 Y,  5 M,  5 C and  5 K of the brand new process cartridge  6 Y,  6 M,  6 C and  6 K includes unused developer having a toner-concentration of 8 wt %. 
   The controller  150  changes the external-input voltage Vcnt of the T-sensors  56 Y,  56 M,  56 C, and  56 K so that each output voltage Vt of the T-sensors  56 Y,  56 M,  56 C, and  56 K becomes 2.5v with respect to the developer having the toner-concentration of 8 wt % for each color. The controller  150  stores the external-input voltage Vcnt during the correction process of the T-sensors  56 Y,  56 M,  56 C, and  56 K. When T-sensors  56 Y,  56 M,  56 C, and  56 K perform detection, the controller  150  sets the external-input voltage Vcnt of the T-sensors  56 Y,  56 M,  56 C, and  56 K with the stored Vcnt values. 
   During a normal printing operation, the toner-concentration of the developer  53  in the developing unit  5  is detected by the T-sensors  56 Y,  56 M,  56 C, and  56 K. The controller  150  controls toner supply units  32 Y,  32 M,  32 C, and  32 K to supply toner to the developing units  5 Y,  5 M,  5 C, and  5 K by controlling the drive motors  41 Y,  41 M,  41 C, and  41 K of the toner supply units  32 Y,  32 M,  32 C, and  32 K respectively in accordance with differences between each output voltage Vt and target value Vtref of the T-sensors  56 Y,  56 M,  56 C, and  56 K. 
   More specifically, the controller  150  determines a toner supply amount based on following formulas (1) and (2). The controller  150  controls the toner supply units  32 Y,  32 M,  32 C, and  32 K to supply toner to the developing units  5 Y,  5 M,  5 C, and  5 K by driving toner drive motors (not shown) of the toner supply units  32 Y,  32 M,  32 C, and  32 K respectively based on the toner supply amount determined by the formulas (1) and (2). 
   When Vt&gt;Vtref,
 
Toner supply amount=α×( Vt−Vtref )/(sensitivity of  T -sensor)  (1)
 
When Vt&lt;Vtref,
 
Toner supply amount=0  (2)
 
   where α is a proportional constant which defines a response of the toner supply amount to the toner-concentration detection of the T-sensors  56 Y,  56 M,  56 C, and  56 K. In the first exemplary embodiment of the disclosure, α is 0.3. 
     FIG. 7  is a graph representing a relationship between the toner-concentration TC and the output voltage Vt of the T-sensors  56 Y,  56 M,  56 C, and  56 K. When the toner-concentration is in a low region, Vt is saturated at 5v as shown in  FIG. 7 . Therefore, it is not possible to detect the toner-concentration accurately. Meanwhile, when the toner-concentration is in a high region, Vt is saturated at 0v as shown in  FIG. 7 . Therefore, it is also not possible to detect the toner-concentration accurately. 
   When the toner-concentration is in the low region, i.e. Vt is at a predetermined Vt or more, but is saturated, the controller  150  uses a different Vcnt value by replacing the Vcnt value obtained with the brand-new developer. 
   In the first exemplary embodiment of the disclosure, when the toner-concentration of the two-component toner is changed significantly from the toner-concentration of the unused developer to a Vt value, for example, Vt&gt;4.0v, the controller  150  uses a lower Vcnt value by 0.2v different from the Vcnt value obtained with the brand-new developer. Namely, the controller  150  takes 3.6v as the Vcnt value. With this change, it becomes possible to detect the toner-concentration at the lower region of the toner-concentration. 
   Meanwhile, when the toner-concentration is in the high region, i.e. Vt is at a predetermined Vt or less but is saturated, the controller  150  uses a different Vcnt value by replacing the Vcnt value from the Vcnt value obtained when the cartridges  6 Y,  6 M,  6 C, and  6 K are exchanged with the brand-new cartridges. In this case, the controller  150  uses a higher value by 0.2v than the initial setting value oppositely to the case in which the toner-concentration is in the low region. Namely, the controller  150  takes 4.0v as the Vcnt value to detect Vt. With this change, it becomes possible to detect the toner-concentration at the high region of the toner-concentration in which Vt was not detected due to a saturation of the Vt value. 
   When the Vcnt value changes, the Vt value also changes as shown in  FIG. 7 . Therefore, correction of the Vt value is necessary to match a shifted Vcnt value. There may still be some variation among the permeability sensors. However, a relationship between the Vcnt and Vt values is approximately constant as shown in  FIG. 8 . 
   The controller  150  performs correction of the Vt value based on a formula (3),
 
( Vt  after correction)=(detected value of  Vt )−Δ Vcnt×S   (3)
 
   where ΔVcnt is a variation of the Vcnt value when the toner-concentration changes, and S is a slope of a data line (Vt vs Vcnt) of  FIG. 8 . In this exemplary embodiment, S is 4.0. 
   Thus, the controller  150  performs correction of the Vt value so that the relationship between the toner-concentration and the Vt value has a linear relationship in a wide range from a low toner-concentration to a high toner-concentration shown as a line expressed by “Vt value after correction as formula (3)” in  FIG. 7 . As a result, the toner-concentration can be determined with one relationship regarding the Vt value. 
   According to the first exemplary embodiment, the printer has an adjusting mode which can cancel the output variation by adjusting the external-input voltage Vcnt. The T-sensors  56 Y,  56 M,  56 C, and  56 K are toner-concentration sensors. Initially, the T-sensors  56 Y,  56 M,  56 C, and  56 K detect the toner-concentration by changing the external-input voltage of the T-sensors  56 Y,  56 M,  56 C, and  56 K under a constant toner-concentration using unused two-component developer. 
   The output signal of the toner-concentration sensor is corrected by changing the external-input voltage based on the relationship between T-sensors  56 Y,  56 M,  56 C, and  56 K versus the external-input voltage when the toner-concentration of the two-component toner deviates from the toner-concentration of the unused developer. 
   Thus, the T-sensors  56 Y,  56 M,  56 C, and  56 K are corrected by the external-input voltage so that the T-sensors  56 Y,  56 M,  56 C, and  56 K output an appropriate toner-concentration detection signal. The output of the T-sensors  56 Y,  56 M,  56 C, and  56 K does not saturate even when the deviation of the toner-concentration of the two-component toner is large. As a result, it is possible to detect the toner-concentration accurately. 
   As another image forming apparatus using the electrophotographic method, a printer according to a second exemplary embodiment will be described. The controller  150  obtains a slope S of the linearity between Vcnt and Vt values shown in  FIG. 8  during a correction process of the T-sensors  56 Y,  56 M,  56 C, and  56 K by changing the external-input voltage Vcnt to the T-sensors  56 Y,  56 M,  56 C, and  56 K so that each output voltage Vt of the T-sensors  56 Y,  56 M,  56 C, and  56 K becomes 2.5v with respect to the developer having 8 wt %. 
   While obtaining Vt values, as shown by the plot in  FIG. 8 , in the correction process, the controller  150  performs approximation for the plot in a linear region of Vcnt and Vt using the least-square method. The calculated slope is defined as S. Thus, the slope S is obtained directly. As a result, the Vt variation of the T-sensors  56 Y,  56 M,  56 C, and  56 K can be reduced and the detection accuracy is improved. 
   According to the second exemplary embodiment, the T-sensors  56 Y,  56 M,  56 C, and  56 K detect the toner-concentration by changing the external-input voltage under a constant toner-concentration. The output voltage of the toner-concentration sensor of T-sensors  56 Y,  56 M,  56 C, and  56 K to the external-input voltage Vcnt are stored. (correction mode of the T-sensors  56 Y,  56 M,  56 C, and  56 K) 
   The controller  150  is a toner-concentration-sensor-output-correction mechanism and controls the change to the external-input voltage based on the relationship between the output voltage of T-sensors  56 Y,  56 M,  56 C, and  56 K to the external-input voltage Vcnt stored in RAM  150   b , when the toner-concentration of the two-component toner deviates from the toner-concentration of the unused developer. The controller  150  performs the correction of the output voltage of the T-sensors  56 Y,  56 M,  56 C, and  56 K. As a result, it is possible to detect the toner-concentration more accurately by detecting the Vt variation at the change of Vcnt value. 
   Further, according to the first and second exemplary embodiments, the controller  150  performs output voltage correction of the T-sensors  56 Y,  56 M,  56 C, and  56 K by changing the external-input voltage when the permeability of the two-component developer deviates from the permeability of the unused developer. Even if the permeability change of the two-component toner is large, the output voltage of the T-sensors does not saturate. As a result, it is possible to detect the toner-concentration accurately. 
   As another image forming apparatus using the electrophotographic method, a printer according to a third exemplary embodiment will be described. The printer according to the third exemplary embodiment changes the Vcnt value when the printer changes a linear velocity. If the printer changes the linear velocity from a normal velocity down to a half velocity keeping the Vcnt value, the apparent permeability of the two-component toner increases. As a result, Vt is saturated in the low toner-concentration, as shown in  FIG. 9 , and the actual toner-concentration cannot be detected. 
   When the process linear velocity is changed from the normal linear velocity of 155 mm/sec down to the half linear velocity of 75.5 mm/sec, the controller  150  sets the Vcnt value with a lower value than a predetermined Vcnt value at the normal linear velocity, in accordance with a linear-velocity-exchange signal sent from a linear-velocity-exchange unit, to match a relationship between the toner-concentration and the Vt value at the normal linear velocity. 
   In this case, changing the amount of Vcnt may not be applied to Δvcnt of formula (3). Then, a similar toner-concentration detection range can be obtained independently of the process linear velocity. 
   According to the third exemplary embodiment, the controller  150  performs a correction of the output voltage of the T-sensors  56 Y,  56 M,  56 C, and  56 K by changing the external-input voltage when the process linear velocity changes. As a result, it is possible to detect the toner-concentration accurately at the change of linear velocity without saturation of the output voltage of the T-sensors  56 Y,  56 M,  56 C, and  56 K. 
   As another image forming apparatus using the electrophotographic method, a printer according to a fourth exemplary embodiment will be described. The printer according to the fourth exemplary embodiment changes the Vcnt value when an environment sensor (not shown) detects a change of temperature and humidity. 
   If the environment in which the image forming apparatus operates becomes a high temperature and a high humidity environment, the apparent permeability of the two-component toner increases. Meanwhile, if it becomes a low temperature and a low humidity environment, an apparent permeability of the two-component toner decreases. As a result, the toner-concentration cannot be detected in the high toner-concentration at the high temperature and high humidity environment and cannot be detected in the low toner-concentration at the low temperature and low humidity environment as shown in  FIG. 10 . 
   The controller  150  sets the Vcnt value to a lower value at the high temperature and high humidity environment and sets the Vcnt value to a predetermined higher value at the low temperature and low humidity environment in accordance with a detection signal from the environment sensor. With this setting, a relationship between the toner-concentration and the Vt value at the high and temperature and high humidity environment becomes a similar relationship to the normal temperature and normal humidity environment. Similarly, a relationship between the toner-concentration and the Vt value at the low temperature and low humidity environment becomes similar to the relationship at the normal temperature and normal humidity environment. 
   In these cases, changing the amount of Vcnt may not be applied to ΔVcnt of formula (3). Then, a similar toner-concentration detection range can be obtained independently of the temperature and humidity. 
   According to the fourth exemplary embodiment, the controller  150  performs a correction of the output voltage of the T-sensors  56 Y,  56 M,  56 C, and  56 K by changing the external-input voltage when the temperature and humidity changes. As a result, it is possible to detect the toner-concentration accurately when the temperature and humidity change without saturation of the output voltage of the T-sensors  56 Y,  56 M,  56 C, and  56 K. 
   As another image forming apparatus using the electrophotographic method, a printer according to a fifth exemplary embodiment will be described. The printer according to the fifth exemplary embodiment changes the Vcnt value in accordance with an image area ratio. The image area ratio is a ratio of the image to be transferred onto paper, or the electrostatic latent image to be developed, or the image input to the developing unit with respect to an area of a paper. 
   If the image area ratio is high, the apparent permeability of the two-component toner increases. Meanwhile, if the image area ratio is low, the apparent permeability of the two-component toner decreases. As a result, the toner-concentration cannot be detected in the high toner-concentration at the high image area ratio and cannot be detected in the low toner-concentration at the low image area ratio, as shown in  FIG. 11 . 
   The controller  150  calculates the image area ratio from the image data input or transmitted to the developing unit  7 . The controller  150  defines a calculated image area ratio as the image area ratio on the paper. 
   The controller  150  performs a correction of the Vcnt value with a predetermined lower value when the image area ratio is higher than a first predetermined value, and performs a correction of the Vcnt value with a predetermined higher value when the image area ratio is lower than a second predetermined value. With this setting, the relationship between the toner-concentration and the Vt value at deviated image area ratios becomes the relationship at the normal image area ratio. 
   In these cases, changing the amount of Vcnt may not be applied to ΔVcnt of formula (3). Then, a similar toner-concentration detection range can be obtained independently on the image area ratio. 
   According to the fifth exemplary embodiment, the controller  150  performs a correction of the output voltage of the T-sensors  56 Y,  56 M,  56 C, and  56 K by changing the external-input voltage in accordance with the image area ratio. As a result, it is possible to detect the toner-concentration accurately even at a large change of the toner-concentration due to a change of the image area ratio without saturation of the output voltage of the T-sensors  56 Y,  56 M,  56 C, and  56 K. 
   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.