Patent Publication Number: US-6658221-B2

Title: Method of and apparatus for measuring quantity of toner on belt-shaped image carrier

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a toner quantity measuring method and a toner quantity measuring apparatus which measure the quantity of toner adhering on a belt-shaped image carrier which is stretched across a plurality of rollers, and an image forming apparatus which comprises such a toner quantity measuring apparatus. 
     2. Description of the Related Art 
     Among image forming apparatuses of the electrophotographic type, such as a printer, a copier machine and a facsimile machine, are those which create a toner image on a belt-shaped image carrier. For example, in an apparatus which is described in Japanese Patent Application Unexamined Gazette No. H11-258872, four process units are disposed along a transfer belt (belt-shaped image carrier) which is stretched across two rollers. Each process unit creates a latent image on a photosensitive member, and the latent image is developed with toner to thereby form a toner image. The toner images thus formed by these process units have different toner colors from each other (yellow, cyan, magenta, black), and transferred onto the transfer belt so that they are laid one atop the other. A color image is created on the transfer belt in this manner. 
     Further, in this apparatus, for the purpose of forming an image with a stable density by means of adjustment of the image densities of toner images, toner images having predetermined patterns (patch images) are formed on the transfer belt and the densities of these patterns are measured with a density sensor. The density sensor comprises a light emitting element which irradiates light upon the transfer belt and a light receiving element which receives light which is reflected by the transfer belt. A controller for controlling the apparatus calculates the quantity of toner adhering to the transfer belt based on an output from the light receiving element and accordingly measures the image densities of toner images. 
     By the way, there has not been any particular attention paid so far to the position at which the density sensor is arranged, and as a result, a sensor output contains various types of noise components and the accuracy of measuring a toner quantity deteriorates. In the conventional apparatus described above, for instance, since the density sensor is disposed at a position which is relatively far from the rollers, there are following problems. 
     At a position far from the rollers as described above, the transfer belt flaps in a direction which is approximately perpendicular to a direction in which the belt travels. Therefore, a distance (hereinafter referred to as “a sensing distance”) from the sensor to the transfer belt (belt-shaped image carrier) changes at random or in an instable manner, and a sensor output becomes instable because of the varying distance. This results in difficulty in conducting accurate measurement. 
     In addition, the transfer belt is stretched across the plurality of rollers and some rollers are eccentric to no small extent. Because of this, the transfer belt flaps even more as the eccentric rollers rotate, which makes a sensor output instable and accurate measurement difficult. 
     Further, the thickness of the transfer belt is not uniform all over the entire circumference of the transfer belt but may be uneven. This acts as one factor which changes the sensing distance. 
     Still further, the quantity of light which is reflected by the transfer belt is influenced not only by toner images formed on the transfer belt but by the condition of a surface of the transfer belt as well. Particularly when the condition of the surface of the transfer belt, e.g., the reflectance and the surface roughness, is not uniform, one can not ignore an influence by the surface condition. 
     SUMMARY OF THE INVENTION 
     A principal object of the present invention is to provide a toner quantity measuring apparatus and a toner quantity measuring method which allow to highly accurate measure the quantity of toner adhering to a belt-shaped image carrier in a structure that the belt-shaped image carrier is stretched across a plurality of rollers. 
     Another object of the present invention is to provide a surface condition detecting method which allows to precisely detect the condition of a surface of a belt-shaped image carrier such as a transfer belt and a photosensitive belt. 
     Yet another object of the present invention is to provide an image forming apparatus which forms an image with a stable density based on a result of measurement conducted with a toner quantity measuring apparatus or by a toner quantity measuring method. 
     The present invention is direct to an apparatus for and a method of measuring the quantity of toner adhering on a belt-shaped image carrier which is stretched across a plurality of rollers. The apparatus comprises: a sensor irradiates light upon the belt-shaped image carrier, and receives light reflected by the belt-shaped image carrier and outputs a signal which corresponds to the quantity of the received light; and toner quantity deriving means calculates the quantity of the toner adhering to the belt-shaped image carrier based on the output from the sensor. 
     The sensor comprises a light emitting element which irradiates light upon the belt-shaped image carrier. The light emitting element is positioned to face one of the plurality of rollers across the belt-shaped image carrier, and irradiates light upon a wind area, out of a surface area of the belt-shaped image carrier, in which the belt-shaped image carrier rests on a sensor-facing roller which is positioned to face the light emitting element. 
     The toner quantity deriving means samples an output signal from the sensor while the belt-shaped image carrier rotates and travels, calculates eccentric components of the roller based on a sampling output, removes the eccentric components from the sampling output and accordingly calculates a periodic profile which is indicative of the condition of a surface of the belt-shaped image carrier, and for calculation of the image density of a toner image on the belt-shaped image carrier, using the eccentric components and the periodic profile, the toner quantity deriving means corrects the output from the light receiving element which receives light reflected by the belt-shaped image carrier and calculates the image density of the toner image based on a correction value. 
     In the case that the length of the circumference of the belt-shaped image carrier is an integer multiple of the length of the circumference of one of the rollers, and the belt-shaped image carrier rotates one round while the one of the rollers rotates two or more rounds, before a toner image is formed on the belt-shaped image carrier, the toner quantity deriving means samples the output signal from the sensor while the belt-shaped image carrier rotates and travels and calculates eccentric components of the roller based on a sampling output. Thereafter, for calculation of the image density of the toner image on the belt-shaped image carrier, using the eccentric components, the toner quantity deriving means corrects the output from the sensor which receives light reflected by the belt-shaped image carrier and calculates the image density of the toner image based on a correction value. 
     The above and further objects and novel features of the invention will more fully appear from the following detailed description when the same is read in connection with the accompanying drawing. It is to be expressly understood, however, that the drawing is for purpose of illustration only and is not intended as a definition of the limits of the invention. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a drawing of a preferred embodiment of an image forming apparatus according to the present invention; 
     FIG. 2 is a drawing of a structure of a sensor which detects the quantity of toner which is on an intermediate transfer belt; 
     FIG. 3 is a drawing of an electric structure of a light receiving unit used in the apparatus shown in FIG. 1; 
     FIG. 4 is a drawing of a light quantity control characteristic in the apparatus shown in FIG. 1; 
     FIG. 5 is a graph showing a change in output voltage with respect to the quantity of reflected light in the apparatus shown in FIG. 1; 
     FIG. 6 is a flow chart showing the sequence of deriving eccentric components and a periodic profile prior to measurement of an actual toner quantity; 
     FIG. 7 is a graph showing one example of sampling data outputted from a sensor; 
     FIG. 8 is a graph showing a periodic profile of an intermediate transfer belt which is obtained by removing eccentric components of a driving roller from the sampling data shown in FIG. 7; 
     FIG. 9 is a flow chart of a toner quantity measuring operation (first preferred embodiment) in the image forming apparatus shown in FIG. 1; 
     FIG. 10 is a flow chart of a toner quantity measuring operation (second preferred embodiment) in the image forming apparatus shown in FIG. 1; 
     FIG. 11 is a flow chart showing the sequence of deriving eccentric components and a periodic profile prior to measurement of an actual toner quantity in a third preferred embodiment; 
     FIG. 12 is a graph showing a periodic profile of an intermediate transfer belt which is obtained in accordance with the derivation sequence shown in FIG. 11; 
     FIG. 13 is a flow chart of a toner quantity measuring operation (third preferred embodiment) in the image forming apparatus shown in FIG. 
     FIG. 14 is a flow chart showing the sequence of deriving eccentric components prior to measurement of an actual toner quantity in a fourth preferred embodiment; 
     FIG. 15 is a graph showing one example of sampling data outputted from a sensor in the fourth preferred embodiment; 
     FIG. 16 is a schematic diagram for describing the sequence of deriving eccentric components in the fourth preferred embodiment; 
     FIG. 17 is a schematic diagram for describing the sequence of deriving eccentric components in a modification; 
     FIG. 18 is a flow chart of a toner quantity measuring operation (fourth preferred embodiment) in the image forming apparatus shown in FIG. 1; 
     FIG. 19 is a schematic diagram for describing the sequence of correcting sampling data in the fourth preferred embodiment; 
     FIG. 20 is a graph showing sampling data corresponding an intermediate transfer belt without patch images, a profile of eccentric components of rollers and a periodic profile in a fifth preferred embodiment; and 
     FIG. 21 is a graph showing sampling data corresponding the intermediate transfer belt with patch images, the profile of eccentric components of rollers, a periodic profile in a fifth preferred embodiment and a profile of a correction value. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     FIG. 1 is a drawing of a preferred embodiment of an image forming apparatus according to the present invention. This image forming apparatus is an apparatus which overlays toner images in four colors of yellow (Y), cyan (C), magenta (M) and black (K) one atop the other and creates a full-color image. As a control unit (denoted generally at 1 in FIG. 2) receives an image signal from an external apparatus such as a host computer, an image corresponding to the image signal is created on a sheet S, such as a transfer paper, a copier paper and a transparency for an overhead projector, with the respective portions of an engine part E operating under the control of the control unit. 
     In the engine part E, it is possible to form a toner image on a photosensitive member  21  of a process unit  2 . In other words, the process unit  2  comprises the photosensitive member  21  which can rotate in the direction indicated by the arrow in FIG.  1 . Further, an electrifying roller  22  serving as electrifying means, developers  23 Y,  23 C,  23 M and  23 K serving as developing means, and a cleaner blade  24  for photosensitive member are disposed around the photosensitive member  21  and along the direction of rotations of the photosensitive member  21 . 
     In this apparatus, after the electrifying roller  22  uniformly electrifies an external circumferential surface of the photosensitive member  21  while staying in contact with the outer circumferential surface of the photosensitive member  21 , an exposure unit  3  irradiates laser light L toward the outer circumferential surface of the photosensitive member  21 . As shown in FIG. 1, the exposure unit  3  comprises a light emitting element  31  such as a semiconductor laser which is modulated as driven in response to the image signal, and laser light L from the light emitting element  31  is incident upon a polygon mirror  33  which is driven to rotate by a high-speed motor  32 . The laser light L reflected by the polygon mirror  33  sweeps over the photosensitive member  21  in a main scanning direction (a direction which is perpendicular to the plane of the drawing) through a lens  34  and a mirror  35 , whereby an electrostatic latent image which corresponds to the image signal is formed. Denoted at  36  is a horizontal synchronization reader sensor for obtaining a synchronizing signal in the main scanning direction. 
     The electrostatic latent image thus created is developed with toner by a developer part  23 . In short, the developer  23 Y for yellow, the developer  23 C for cyan, the developer  23 M for magenta and the developer  23 K for black are arranged as the developer part  23  in this order along the photosensitive member  21 , according to this embodiment. The developers  23 Y,  23 C,  23 M and  23 K are each capable of freely abutting on and departing from the photosensitive member  21 . In response to an instruction from the control unit  1 , one of the four developers  23 Y,  23 C,  23 M and  23 K selectively contacts the photosensitive member  21 , supplies toner of a selected color to a surface of the photosensitive member  21  by means of an applied high voltage, and visualizes the electrostatic latent image on the photosensitive member  21 . 
     The toner image developed by the developer part  23  is primarily transferred, in a primary transfer area located between the black developer  23 K and the cleaner blade  24  for photosensitive member, onto an intermediate transfer belt  41  (belt-shaped image carrier) of a transfer unit  4 . Further, the cleaner blade  24  for photosensitive member is disposed at a position ahead of the primary transfer area in a circumferential direction (which is the direction indicated at the arrow in FIG.  1 ), and scrapes off the toner still sticking to the outer circumferential surface of the photosensitive member  21  after the primary transfer. 
     The transfer unit  4  comprises seven rollers  42  to  48 , and the endless intermediate transfer belt  41  is stretched across the six rollers  42  to  47  except for the secondary transfer roller  48 . For transfer of a color image onto a sheet S, toner images of the respective colors formed on the photosensitive member  21  are laid one atop the other on the intermediate transfer belt  41  thereby forming a color image, during which the sheet S unloaded from a cassette or a hand-feed tray travels to a secondary transfer area moving passed between an upper guide member  5 U and a lower guide member  5 D, whereby the color image is secondarily transferred onto the sheet S and the color image is obtained (color printing process). Meanwhile, for transfer of a monochrome image onto a sheet S, only a black toner image on the photosensitive member  21  is formed on the intermediate transfer belt  41  and thereafter transferred onto a sheet S conveyed to the secondary transfer area in a manner similar to that for a color image, whereby the monochrome image is obtained (monochrome printing process). 
     A belt cleaner  49  is disposed facing the roller  46 . The belt cleaner  49  is for removing and cleaning off residual toner which remain on the intermediate transfer belt  41  after the secondary transfer, and has a structure as described below. In short, in the belt cleaner  49 , a cleaner blade  492  is attached to a cleaner case  491  in such a manner that the cleaner blade  492  can abut on and move away from the intermediate transfer belt  41  inside a cleaner cover  493 , and the cleaner blade  492  is driven by a belt cleaner driver part (not shown) to abut on and move away from the intermediate transfer belt. Denoted at  494  in FIG. 1 is a cleaner scoop sheet. 
     A sensor  40  for detecting a reference position of the intermediate transfer belt  41  is disposed at a position below the roller  43 , to serve as a vertical synchronization reader sensor for obtaining a synchronizing signal in a sub scanning direction which is approximately perpendicular to the main scanning direction, i.e., a vertical synchronizing signal. Meanwhile, a sensor  6  for detecting the quantity of toner adhering on the intermediate transfer belt  41  which is spun over the roller  43 , is disposed so as to face the roller  43  across the intermediate transfer belt  41 . Thus, the roller  43  in this embodiment is a “sensor-facing roller” of the present invention. 
     FIG. 2 is a drawing of a structure of the sensor which detects the quantity of toner on the intermediate transfer belt. This sensor  6  comprises a light emitting element  601  such as an LED which irradiates light upon a wind area  41   a  resting on the roller  43  out of a surface area of the intermediate transfer belt  41 . Further, in order to adjust the quantity of irradiated light, the sensor  6  comprises a polarizing beam splitter  603 , an irradiation quantity monitoring light receiving unit  604  and an irradiation quantity adjusting unit  605 . 
     The polarizing beam splitter  603  is located between the light emitting element  601  and the intermediate transfer belt  41  as shown in FIG. 2, and splits light into p-polarized light whose polarization direction is parallel to a surface of incidence in which the irradiated light impinges on the intermediate transfer belt  41  and s-polarized light whose polarization direction is perpendicular to the surface of incidence. While the p-polarized light directly impinges upon the intermediate transfer belt  41 , the s-polarized light enters the irradiation quantity monitoring light receiving unit  604  after leaving the polarizing beam splitter  603  so that a signal, which is in proportion to the quantity of the irradiated light from the light receiving unit  604 , is outputted to the irradiation quantity adjusting unit  605 . 
     Based on the signal from the light receiving unit  604  and a light quantity control signal S 1 c provided from the control unit  1  which comprises a CPU  11  and a memory  12  and controls the apparatus as a whole, the irradiation quantity adjusting unit  605  feedback-controls the light emitting element  601 , whereby the quantity of the irradiated light from the light emitting element  601  illuminating the intermediate transfer belt  41  is adjusted to a value which corresponds to the light quantity control signal S 1 c. In this manner, this embodiment permits to change and adjust the quantity of irradiation in a wide range. 
     Further, according to this embodiment, an input offset voltage  641  is applied to the output side of a light receiving element  642  which is disposed to the irradiation quantity monitoring light receiving unit  604 , and therefore, the light emitting element  601  is maintained turned off unless the light quantity control signal S 1 c exceeds a certain signal level. A specific electric structure of this is as shown in FIG.  3 . FIG. 3 is a drawing of an electric structure of the light receiving unit  604  used in the apparatus shown in FIG.  1 . In the light receiving unit  604 , an anode terminal of a light receiving element PS such as a photodiode is connected with a non-inversion input terminal of an operational amplifier OP which forms a current/voltage (I/V) circuit and grounded through the input offset voltage  641 . Meanwhile, a cathode terminal of the light receiving element PS is connected with an inversion input terminal of the operational amplifier OP and also with an output terminal of the operational amplifier OP through a resistor R. Hence, as the light receiving element PS receives light and carries a photoelectric current i, an output voltage V 0  at the output terminal-of the operational amplifier OP is: 
     
       
           V 0= i·R+Voff    
       
     
     (where Voff denotes an offset voltage value) and therefore, a signal corresponding to the quantity of the reflected light is outputted from the light receiving unit  604 . The reason of such a structure will be described in the following. 
     Without application of the input offset voltage  641 , a light quantity characteristic is as indicated at the dotted line in FIG.  4 . That is, as the light quantity control signal S 1 c(0) is supplied to the irradiation quantity adjusting unit  605  from the control unit  1 , the light emitting element  601  turns off. The light emitting element  601  turns on when the signal level of the light quantity control signal S 1 c increases, and the quantity of the irradiated light upon the intermediate transfer belt  41  as well increases in approximate proportion to the signal level. However, the light quantity characteristic sometimes shifts parallel as indicated at the dotted-and-dashed line or the double-dotted-and-dashed line in FIG. 4 due to an influence of an ambient temperature, the structure of the irradiation quantity adjusting unit  605 , etc. Once a shift as that denoted at the dotted-and-dashed line in FIG. 4 for instance occurs, the light emitting element  601  may stay turned on despite a turn-off instruction, namely, the light quantity control signal S 1 c( 0 ) from the control unit  1 . 
     In contrast, the embodiment has a dead zone. More specifically, a shift toward the right-hand side in FIG. 4 is provided in advance by means of application of the input offset voltage  641  and the dead zone (signal levels S 1 c( 0 ) to S 1 c( 1 )) is consequently created as in this embodiment (as indicated at the solid line in FIG.  4 ). With the turn-off instruction, namely, the light quantity control signal S 1 c( 0 ) supplied from the control unit  1 , it is possible to turn off the light emitting element  601  without fail, and hence, prevent malfunction of the apparatus. 
     On the other hand, when the light quantity control signal S 1 c exceeding the signal level S 1 c( 1 ) is supplied to the irradiation quantity adjusting unit  605  from the control unit  1 , the light emitting element  601  turns on and p-polarized light is irradiated as irradiation light toward the intermediate transfer belt  41 . The intermediate transfer belt  41  reflects the p-polarized light, a reflection quantity detecting unit  607  detects the quantities of the p-polarized light and the s-polarized light among light components of the reflected light, and signals corresponding to the respective light quantities are outputted to the control unit  1 . 
     As shown in FIG. 2, the reflection quantity detecting unit  607  comprises a polarizing beam splitter  671  which is disposed on an optical path of the reflected light, a light receiving unit  670   p  which receives the p-polarized light traveling through the polarizing beam splitter  671  and outputs a signal corresponding to the quantity of the p-polarized light, and a light receiving unit  670   s  which receives the s-polarized light split by the polarizing beam splitter  671  and outputs a signal corresponding to the quantity of the s-polarized light. In the light receiving unit  670   p , a light receiving element  672   p  receives the p-polarized light from the polarizing beam splitter  671 , and after the output signal from the light receiving element  672   p  is amplified by an amplifier circuit  673   p , the light receiving unit  670   p  outputs the amplified signal as a signal which corresponds to the quantity of the p-polarized light. Further, like the light receiving unit  670   p , the light receiving unit  670   s  comprises a light receiving element  672   s  and an amplifier circuit  673   s . Hence, it is possible to independently calculate the light quantities of two light components (i.e., the p-polarized light and the s-polarized light) which are different from each other among light components of the reflected light. 
     Further, in this embodiment, output offset voltages  674   p ,  674   s  are applied respectively to the output side of the light receiving elements  672   p ,  672   s , and output voltages Vp, Vs of signals supplied to the control unit  1  from the amplifier circuits  673   p ,  673   s  are offset to the positive side as shown in FIG.  5 . Specific electric structures of the respective light receiving units  670   p ,  670   s  are the same as that of the light receiving unit  604 , and therefore, will not be shown in the drawings or described again. In the light receiving units  670   p ,  670   s  having such structures as well, the output voltages Vp, Vs each have a value which is equal to or larger than zero even when the quantity of the reflected light is zero, and moreover, the output voltages Vp, Vs increase proportionally as the quantity of the reflected light increases, which is similar as in the light receiving unit  604 . In this manner, with application of output offset voltages  674   p ,  674   s , it is possible to eliminate an influence of the dead zone which is shown in FIG. 4 without fail and output an output voltage which corresponds to the quantity of the reflected light. 
     The signals having the output voltages Vp, Vs are supplied to the control unit  1  which functions as toner quantity deriving means and A/D-converted, after which the control unit  1  calculates the quantity of toner adhering on the intermediate transfer belt  41 . According to the present invention, there are different methods of measuring a toner quantity in accordance with the following characteristics in structure of the apparatus: 
     (a) Whether the length of the circumference of the intermediate transfer belt  41  which corresponds to the “belt-shaped image carrier” is an integer multiple or a non-integer multiple of the length of the circumference of the sensor-facing roller  43 ; 
     (b) Whether the thickness of the intermediate transfer belt  41  is even or not; and 
     (c) Whether the condition of a surface of the intermediate transfer belt  41  is uniform or not. 
     Now, each one of these will be described. 
     A. First Preferred Embodiment 
     First, a description will be given on a method of measuring a toner quantity in an image forming apparatus in which the length of the circumference of the intermediate transfer belt  41  is a non-integer multiple of the length of the circumference of the sensor-facing roller  43  and the thickness of the intermediate transfer belt  41  is not even. 
     FIG. 6 is a flow chart showing the sequence of deriving eccentric components and a periodic profile prior to measurement of an actual toner quantity. In this apparatus, the control unit  1  provides the irradiation quantity adjusting unit  605  with the light quantity control signal S 1 c( 0 ) which corresponds to the turn-off instruction and turns off the light emitting element  601  (Step S 1 ). According to this embodiment in particular, as described above, since the dead zone (signal level S 1 c( 0 ) to S 1 c( 1 ) in FIG. 4) is set up by means of application of the input offset voltage  651 , and therefore, the light emitting element  601  upon receipt of the light quantity control signal S 1 c( 0 ) turns off without fail. 
     An output voltage Vp 0  which is indicative of the received quantity of the p-polarized light and an output voltage Vs 0  which is indicative of the received quantity of the s-polarized light in this OFF-state are detected and stored in the memory  12  of the control unit  1  (Step S 2 ). In short, a sensor output in the OFF-state, namely, dark output voltages Vpo, Vso are detected and stored. 
     Next, a signal S 1 c( 2 ) at a signal level beyond the dead zone is set as the light quantity control signal S 1 c, and this light quantity control signal S 1 c( 2 ) is supplied to the irradiation quantity adjusting unit  605  to thereby turn on the light element  601  (Step S 3 ). This causes light from the light emitting element  601  to irradiate upon the intermediate transfer belt  41 , the reflection quantity detecting unit  607  to detect the quantities of the p-polarized light and the s-polarized light which are reflected by the intermediate transfer belt  41 , and the control unit  1  to receive the output voltages Vp, Vs which correspond to the respective received light quantities (Step S 4 ). 
     The control unit  1  subtracts the dark output voltage Vp 0  from the output voltage Vp with respect to the p-polarized light, thereby calculating a light quantity signal SigP which represents the quantity of the p-polarized light which corresponds to the toner quantity (Step S 5 ). With respect to the s-polarized light as well, similarly to the p-polarized light, the control unit  1  subtracts the dark output voltage Vs 0  from the output voltage Vs to yield a light quantity signal SigS which represents the quantity of the s-polarized light which corresponds to the toner quantity (Step S 5 ). A ratio of the light quantity signals SigP and SigS thus corrected is then calculated as sampling data (Step S 5 ). Since the dark output voltages Vp 0 , Vs 0  are removed from the measured output voltages Vp, Vs according to this embodiment, it is possible to accurately calculate the light quantities which correspond to the toner quantity. Therefore, even when there is a change in dark output due to an environmental condition, such as an ambient temperature around the apparatus, or a change with time of the components which form the apparatus, it is possible to obtain an index regarding the toner quantity without affected by these factors. 
     More precisely, the sampling data are obtained in the following manner. In the image forming apparatus according to this embodiment, the length of the circumference of the intermediate transfer belt  41  is a non-integer multiple of the length of the circumference of the sensor-facing roller  43  and the intermediate transfer belt  41  travels one round for approximately every 5.2 rounds of the sensor-facing roller  43 . It takes 3120 ms for the intermediate transfer belt  41  to make one round. The quantity of reflected light from the intermediate transfer belt  41  is sampled at intervals of 10 ms, the output voltage Vp 0  upon turning off is subtracted from the output voltage Vp as it is at each sampling position x to thereby calculate the light quantity signal SigP (=Vp−Vp 0 ), while the output voltage Vs 0  upon turning off is subtracted from the output voltage Vs as it is at each sampling position x to thereby calculate the light quantity signal SigS (=Vs−Vs 0 ). Following this, ratios of these light quantity signals (=SigP/SigS) are stored in the memory  12  as sampling data D(x) at the respective sampling positions x (FIG.  7 ). In this embodiment, while  312  pieces of sampling data D(x) are obtained while the intermediate transfer belt  41  travels one round, for the purpose of executing efficient calculation using a small memory capacity, the number of samples to take is set to 256. That is, the sampling data D( 0 ), D( 1 ), . . . D( 255 ) are stored in the memory  12 . 
     At the next Step S 6 , eccentric components of the rollers are calculated on the basis of the sampling data D( 0 ), D( 1 ), D( 255 ) and stored in the memory  12 . The details will be now described with reference to FIG.  7 . According to this embodiment, since the intermediate transfer belt  41  travels a round every time the roller  43  makes 5.2 rounds, when consecutive  60  (=312/5.2) pieces of sampling data are extracted from the sampling data D(x) above, the 60 sampling data pieces contain components which correspond to one round of the roller  43 . Now, noting eccentric components of the roller  43 , calculation of an average value representing one round of the sensor-facing roller  43  makes it unnecessary to consider the eccentric components. There is a moment that the sensing distance becomes long and a moment that the sensing distance becomes short while the sensor-facing roller  43  rotates one round, and influences of these are considered to cancel out each other when the average value is calculated. This average value therefore can be viewed approximately equivalent to an average corresponding to a designed sensing distance. 
     Using the consecutive  60  sampling data pieces as one section, three sections (1) to (3) are defined in the sampling data D(x) as shown in FIG. 7, average values AV(x) representing one round of the roller  43  at the sampling positions x (x=30, 31, . . . , 210) constituting the respective sections are calculated. 
     
       
           AV (30)=( D (0)+ . . . + D (30)+ . . . + D (59))/60  
       
     
     
       
           AV (31)=( D (1)+ . . . + D (31)+ . . . + D (60))/60  
       
     
     
       
           AV (32)=( D (2)+ . . . + D (32)+ . . . + D (61))/60  
       
     
     
       
         . . .  
       
     
     
       
           AV (210)=( D (180)+ . . . + D (210)+ . . . + D (239))/60  
       
     
     While the center of the 60 sampling data pieces at the sampling positions “0” through “59” is 30 in the formulas above, the center is between “29” and “30” in a strict sense. Therefore, the formulas above may be as below: 
     
       
           AV (29)=( D (0)+ . . . + D (30)+ . . . + D (59))/60  
       
     
     (and so forth) 
     Thus calculated average values AV(x) are values from which the eccentric components of the roller  43  have been cancelled, and therefore, as the average values AV(x) are subtracted from the sampling data D(x), the eccentric components E(x) of the roller  43  at the respective sampling positions x are calculated. In other words, it is possible to calculate the eccentric components E(x) of the roller  43  by the following: 
     
       
           E ( x )= D ( x )− AV ( x )  
       
     
     With this formula, however, the calculated eccentric components of the roller  43  are those corresponding to three rounds of the roller  43  for every round of the intermediate transfer belt  41 . 
     Since the sections (1) through (3) each correspond to one round of the roller  43 , if the phase remains the same, the eccentric components E(x) must have the same value. Noting this, average values Eav(a) of the eccentric components where the sections (1) through (3) are in the same phase are calculated as follows: 
     
       
           Eav ( a )={ D (30+ a )− AV (30+ a )}+{ D (90+ a )− AV (90+ a )}+{ D (120+ a )− D (120+ a )}/3  (1)  
       
     
     (where a=0, 1, . . . 59) 
     In this manner, according to this embodiment, since three eccentric components are calculated while the intermediate transfer belt  41  travels one round and an average values of these three is then calculated, the eccentric components of the roller  43  are calculated at a high accuracy. Of course, the number of revolutions of the roller  43  per one round of the intermediate transfer belt  41  is not limited to “5.2” but may only be two or more, in which case it is possible to calculate the eccentric components of the roller  43  in the manner similar to the above. 
     As the eccentric components Eav(a) of the roller  43  in the respective phases are calculated by the formula (1) (Step S 6 ), the eccentric components are subtracted from the sampling data D(x), to thereby detect a periodic profile F(x) which reflects evenness in thickness of the intermediate transfer belt  41  (FIG.  8 ). In short, the periodic profile F(x) is as follows: 
     
       
           F (0)= D (0)− Eav (30)  
       
     
     
       
           F (1)= D (1)− Eav (31)  
       
     
     
       
         . . .  
       
     
     
       
           F (29)= D (29)− Eav (59)  
       
     
     
       
           F (30)= D (30)− Eav (0)  
       
     
     
       
           F (31)= D (31)− Eav (1)  
       
     
     
       
         . . .  
       
     
     The periodic profile F(x) is then stored in the memory  12  in preparation for measurement of an actual quantity of toner (Step S 7 ). 
     Next, the sequence of measurement of an actual quantity of toner will be described with reference to FIG.  9 . FIG. 9 is a flow chart showing a toner quantity measuring operation in the image forming apparatus shown in FIG.  1 . In this apparatus, the control unit  1  executes steps (Step S 11  to Step S 15 ) similar to Step S 11  to Step S 5  which are used in the sequence of deriving the eccentric components and the periodic profile, a light quantity signal ratio (=SigP/SigS) which serves as an index regarding a toner quantity is calculated as the sampling data D(x) and stored in the memory  12 . 
     Next, at Step S 16 , the light quantity signal ratio obtained as described above is corrected using the eccentric components Eav(a) and the periodic profile F(x). The sequence of this correction is as described below. 
     First, in this embodiment, every time the sensor-facing roller  43  makes approximately 5.2 rounds, the intermediate transfer belt  41  travels one round. Hence, the sensor-facing roller  43  is in different phases between upon calculation of the eccentric components and the periodic profile above and upon later detection for the purpose of calculation of a toner quantity. However, a ratio between the length of the circumference of the sensor-facing roller  43  and the length of the intermediate transfer belt  41  is known for a design purpose. Noting this, based on how many rounds the intermediate transfer belt  41  has traveled since calculation of the eccentric components and the periodic profile until detection of a toner quantity, the phases of the eccentric components are shifted and matched with the phase of the sensor-facing roller  43  at it is upon toner quantity detection. The periodic profile and the eccentric components are thereafter synthesized, and the light quantity signal ratio is corrected. 
     Through the processing described above, it is possible to correct an influence of the eccentric components of the roller and the uneven thickness of the intermediate transfer belt  41 . The toner quantity is then measured in accordance with the result of the correction (Step S 17 ). 
     As described above, according to this embodiment, after the eccentric components Eav(a) of the roller are calculated from the sampling data D(x), the eccentric components Eav(a) are subtracted from the sampling data D(x) to calculate the periodic profile F(x) (Step S 7 ), and therefore, the periodic profile F(x) which are indicative of the uneven thickness of the intermediate transfer belt  41  do not contain the eccentric components of the roller but accurately represent the uneven thickness of the intermediate transfer belt  41 . 
     Further, the sampling data D(x) obtained for measurement of an actual toner quantity are corrected (Step S 16 ) using thus accurately obtained periodic profile F(x), and the toner quantity is measured in accordance with the correction value (Step S 17 ), and hence, it is possible to improve the accuracy of measuring the toner quantity. 
     In addition, since this embodiment suppresses not only unevenness in thickness of the intermediate transfer belt  41  but also a change in distance (sensing distance) between the sensor  6  and the intermediate transfer belt  41  and corrects a change in distance due to eccentric components of the roller, it is possible to further improve the measuring accuracy. More specifically, this embodiment realizes the following two effects. 
     In the conventional apparatus described above, namely, the apparatus which is described in Japanese Patent Application Unexamined Gazette No. H11-258872, the sensor is located at a position far away from the roller and the intermediate transfer belt  41  dances in a direction which is approximately perpendicular to the direction in which the belt travels. Therefore, the sensing distance between the sensor  6  and the intermediate transfer belt  41  changes at random or in an instable manner, and an output from the sensor becomes instable because of the varying distance. In contrast, according to this embodiment, light irradiates upon the surface area of the intermediate transfer belt where the belt is wound around the roller  43 , i.e., the wind area  41   a , light reflected in the wind area  41   a  is received by the light receiving elements  672   p  and  672   s , and a toner quantity is measured in accordance with the signal which is outputted from the sensor  6 . In the wind area  41   a , it is possible to prevent instable flaps of the intermediate transfer belt  41  in the direction which is approximately perpendicular to the direction in which the belt travels. 
     Further, according to this embodiment, since the eccentric components Eav(a) of the roller are calculated (Step S 6 ) to thereby correct a change in sensing distance between the sensor  6  and the intermediate transfer belt  41  which is attributed to the eccentricity of the roller (Step S 16 ), it is possible to suppress an influence of the eccentricity of the roller and further improve the measuring accuracy. 
     Further, while there is a danger that toner may fall off floating from the intermediate transfer belt  41  and adhere to the sensor  6  during measurement of the quantity of the toner on the intermediate transfer belt  41 . Since the sensor  6  is arranged at a horizontal opposing position with respect to the roller  43  which is the sensor-facing roller, a sensing surface stands vertically, which in turn makes it possible to effectively prevent the floating toner from adhering to the sensing surface and improve the measuring accuracy. This effect remains similar or even improves, even when the sensor  6  is disposed above the horizontal opposing position to the roller  43  (FIG. 2) and at a position opposed to the roller  43 . 
     Further, according to this embodiment, the light quantity signal SigP representing the quantity of the p-polarized light and the light quantity signal SigS representing the quantity of the s-polarized light among the light components of the reflected light from the intermediate transfer belt  41 , are calculated independently of each other, and the quantity of the toner adhering on the intermediate transfer belt  41  is measured based on the light quantity signal ratio (=SigP/SigS). Therefore, a noise, the changing quantity of the irradiated light upon the intermediate transfer belt  41  and the like are not easily influential, and it is possible to measure the toner quantity at a high accuracy. 
     Further, while it is necessary to turn off the light emitting element  601  without fail for calculation of dark outputs, according to this embodiment, as the input offset voltage  651  is applied as described above, the light emitting element  601  turns off without fail. 
     B. Second Preferred Embodiment 
     Next, a description will be given on a method of measuring a toner quantity in an image forming apparatus in which the length of the circumference of the intermediate transfer belt  41  is an integer multiple of the length of the circumference of the sensor-facing roller  43  and the thickness of the intermediate transfer belt  41  is uneven. 
     In an image forming apparatus in which the length of the circumference of the intermediate transfer belt  41  is an integer multiple of the length of the circumference of the sensor-facing roller  43 , as the quantity of toner is measured in the sequence which is shown in FIG. 10, a change in distance (sensing distance) between the sensor  6  and the intermediate transfer belt  41  is suppressed, an influence of eccentric components of the roller and the uneven thickness of the intermediate transfer belt  41  is corrected, and the quantity of toner adhering to the intermediate transfer belt  41  is measured at a high accuracy in a manner similar to that in the first preferred embodiment. 
     FIG. 10 is a flow chart showing a toner quantity measuring operation in an image forming apparatus according to the present invention (second preferred embodiment). The output voltages Vp and Vs which correspond to the quantity of reflected light from the intermediate transfer belt  41  are sampled at predetermined sampling intervals (e.g., 10 ms) while the intermediate transfer belt  41 , which does not bear a toner image, makes one round. After the dark output voltage Vp 0  is subtracted from the output voltage Vp to thereby calculate the light quantity signal SigP representing the quantity of the p-polarized light which corresponds to the quantity of toner while the dark output voltage Vs 0  is subtracted from the output voltage Vs to thereby calculate the light quantity signal SigS representing the quantity of the s-polarized light which corresponds to the quantity of toner as described above. Thereafter, a ratio between thus corrected light quantity signals SigP and SigS is calculated and light quantity signal ratios R(x) at the respective sampling positions x are stored in the memory  12  as foundation data (Step S 21 ). The foundation data R(x) calculated in this manner contain the eccentric components of the roller and the uneven thickness of the belt described in detail above. In addition, since the length of the circumference of the intermediate transfer belt  41  is an integer multiple of the length of the circumference of the sensor-facing roller  43 , there is not a phase difference between the two regardless of the number of rotations. 
     Steps (Step S 22  to Step S 26 ) similar to Step S 1  to Step S 5  according to the first preferred embodiment are executed for measurement of an actual toner quantity, whereby the light quantity signal ratios (=SigP/SigS) which serve as an index regarding a toner quantity are calculated as the sampling data D(x) and stored in the memory  12 . 
     Following this, after the sampling data D(x) are corrected based on the foundation data R(x) (Step S 27 ), the quantity of the toner is detected based on the corrected light quantity signal ratios (Step S 28 ). 
     As described above, according to the second preferred embodiment, the foundation data R(x) are subtracted from the sampling data D(x) and an influence of the eccentric components of the roller and the uneven thickness of the belt is corrected, so that the quantity of the toner adhering to the intermediate transfer belt  41  is measured at a high accuracy. Hence, as compared with the first preferred embodiment, the second preferred embodiment realizes a new effect that highly accurate toner measurement is possible through a fewer processing steps, in addition to the effect obtainable according to the first preferred embodiment. 
     C. Third Preferred Embodiment 
     Next, a description will be given on a method of measuring a toner quantity in an image forming apparatus in which the length of the circumference of the intermediate transfer belt  41  is a non-integer multiple of the length of the circumference of the sensor-facing roller  43  and the condition of a surface of the intermediate transfer belt  41  is not uniform. 
     FIG. 11 is a flow chart showing the sequence of deriving eccentric components and a periodic profile prior to measurement of an actual toner quantity. According to the third preferred embodiment as well, the same processing as that through Step S 1  to Step S 6  according to the first preferred embodiment is executed, and the eccentric components Eav(a) of the roller  43  are calculated and stored in the memory  12 . In the third preferred embodiment, however, since the condition of a surface of the intermediate transfer belt  41  is not uniform while the thickness of the intermediate transfer belt  41  is constant, Step S 8  is executed to thereby yield a periodic profile F′(x) which is indicative of the condition of the surface of the intermediate transfer belt  41 . 
     At Step S 8 , the eccentric components are subtracted from the sampling data D(x) and the periodic profile F′(x) which reflects the condition of the surface of the intermediate transfer belt  41  is detected (See FIG.  12 ). In other words, the periodic profile F′(x) as follow are obtained: 
     
       
           F ′(0)= D (0)− Eav (30)  
       
     
     
       
           F ′(1)= D (1)− Eav (31)  
       
     
     
       
         . . .  
       
     
     
       
           F ′(29)= D (29)− Eav (59)  
       
     
     
       
           F ′(30)= D (30)− Eav (0)  
       
     
     
       
           F ′(31)= D (31)− Eav (1)  
       
     
     
       
         . . .  
       
     
     The periodic profile F′(x) is then stored in the memory  12 , in preparation for measurement of an actual quantity of toner (Step S 8 ). 
     Next, the sequence of measuring an actual quantity of toner will be described with reference to FIG.  13 . FIG. 13 is a flow chart showing a toner quantity measuring operation in the image forming apparatus shown in FIG. 1 (third preferred embodiment). In this apparatus, the control unit  1  executes steps (Step S 31  to Step S 35 ) similar to Step S 1  to Step S 5  which are used in the sequence of deriving the eccentric components and the periodic profile, light quantity signal ratios (=SigP/SigS) which serve as an index regarding a toner quantity are calculated as the sampling data D(x) and stored in the memory  12 . 
     Next, at Step S 36 , the light quantity signal ratios obtained as described above are corrected using the eccentric components Eav(a) and the periodic profile F′(x). The sequence of this correction is as described below. 
     First, in this embodiment, every time the sensor-facing roller  43  makes approximately 5.2 rounds, the intermediate transfer belt  41  travels one round. Hence, the sensor-facing roller  43  is in different phases between upon calculation of the eccentric components and the periodic profile above and upon later detection for the purpose of calculation of a toner quantity. However, a ratio between the length of the circumference of the sensor-facing roller  43  and the length of the intermediate transfer belt  41  is known for a design purpose. Noting this, based on how many rounds the intermediate transfer belt  41  has traveled since calculation of the eccentric components and the periodic profile until detection of a toner quantity, the phases of the eccentric components are shifted and matched with the phase of the sensor-facing roller  43  at it is upon toner quantity detection. The periodic profile and the eccentric components are thereafter synthesized, and the light quantity signal ratios are corrected (Step S 36 ). 
     Through the processing described above, it is possible to correct an influence of the eccentric components of the roller and the condition of the surface of the intermediate transfer belt  41 . The toner quantity is then measured in accordance with the result of the correction (Step S 37 ). 
     As described above, according to this embodiment, after the eccentric components Eav(a) of the roller  43  are calculated from the sampling data D(x), the eccentric components Eav(a) are subtracted from the sampling data D(x) to calculate the periodic profile F′(x) (Step S 36 ), and therefore, the periodic profile F′(x) which is indicative of the condition of the surface of the intermediate transfer belt  41  do not contain the eccentric components of the roller but accurately represent the condition of the surface of the intermediate transfer belt  41 . 
     Further, the sampling data D(x) obtained for measurement of an actual toner quantity are corrected (Step S 36 ) using thus accurately obtained periodic profile F′(x), and the toner quantity is measured in accordance with the correction value (Step S 37 ), and hence, it is possible to improve the accuracy of measuring the toner quantity. 
     In addition, since this embodiment suppresses not only a change in surface condition of the intermediate transfer belt  41  but also a change in distance (sensing distance) between the sensor  6  and the intermediate transfer belt  41  and corrects a distance change due to eccentric components of the roller, it is possible to further improve the measuring accuracy as in the first preferred embodiment. 
     D. Fourth Preferred Embodiment 
     Next, a description will be given on a method of measuring a toner quantity in an image forming apparatus in which the length of the circumference of the intermediate transfer belt  41  is an integer multiple of the length of the circumference of the sensor-facing roller  43 . 
     FIG. 14 is a flow chart showing the sequence of deriving eccentric components prior to measurement of an actual toner quantity in the fourth preferred embodiment. According to the fourth preferred embodiment as well, the same processing as that through Step S 1  to Step S 6  according to the first preferred embodiment is executed, and eccentric components of the roller  43  are calculated and stored in the memory  12 . The fourth preferred embodiment, however, is largely different from the first preferred embodiment with respect to a method of acquiring sampling data. 
     In an image forming apparatus according to the fourth preferred embodiment, the length of the circumference of the intermediate transfer belt  41  which corresponds to the “belt-shaped image carrier” is an integer multiple of the length of the circumference of the sensor-facing roller  43 , and every time the sensor-facing roller  43  makes five rounds, the intermediate transfer belt  41  travels one round. It takes 3000 ms for the intermediate transfer belt  41  to make one round. The quantity of reflected light from the intermediate transfer belt  41  is sampled at intervals of 10 ms, at Step S 45  the output voltage Vp 0  upon turning off is subtracted from the output voltage Vp as it is at each sampling position X to thereby calculate the light quantity signal SigP (=Vp−Vp 0 ), while the output voltage Vs 0  upon turning off is subtracted from the output voltage Vs as it is at each sampling position X to thereby calculate the light quantity signal SigS (=Vs−Vs 0 ). Following this, a ratio between these light quantity signals (=SigP/SigS) is stored in the memory  12  as sampling data D(x) at each sampling position X (FIGS.  15  and  16 ). In this embodiment, the intermediate transfer belt  41  travels one round every time the sensor-facing roller  43  makes five rounds and  300  pieces of sampling data D(x) are obtained during this, for the purpose of calculating eccentric components of the roller  43  using a small memory capacity in a short period of time as described later, 360 pieces of sampling data D( 0 ) to D( 359 ) which are obtained while the roller  43  rotates six rounds are sampled and stored in the memory  12 . 
     Next, at Step S 46 , eccentric components of the roller are calculated from the sampling data D( 0 ), D( 1 ), . . . D( 359 ) and stored in the memory  12 . The details will be now described with reference to FIGS. 15 and 16. According to this embodiment, since the intermediate transfer belt  41  travels one round while the roller  43  rotates five rounds, while consecutive 60 (=300/5) pieces of sampling data are yielded from the sampling data D(x) described above, the 60 sampling data pieces contain components which correspond to one round of the roller  43 . Now, noting eccentric components of the roller  43 , calculation of an average value representing one round of the sensor-facing roller  43  makes it unnecessary to consider the eccentric components. There is a moment that the sensing distance becomes long and a moment that the sensing distance becomes short while the sensor-facing roller  43  rotates one round, and influences of these are considered to cancel out each other when the average value is used. This average value therefore can be viewed approximately equivalent to an average corresponding to a designed sensing distance. 
     Using the consecutive  60  sampling data pieces as one section,  301  sections, i.e., a section D( 0 ) to D( 59 ), a section D( 1 ) to D( 60 ), . . . , a section D( 300 ) to D( 359 ) are defined, and average values AV(x) corresponding to one round of the roller  43  at the center positions X (X=30, 31, . . . , 330) in the respective sections are calculated. 
     
       
           AV (30)=( D (0)+ . . . + D (30)+ . . . + D (59))/60  
       
     
     
       
           AV (31)=( D (1)+ . . . + D (31)+ . . . + D (60))/60  
       
     
     
       
           AV (32)=( D (2)+ . . . + D (32)+ . . . + D (61))/60  
       
     
     
       
         . . .  
       
     
     
       
           AV (330)=( D (300)+ . . . + D (330)+ . . . + D (359))/60  
       
     
     While the center of the 60 sampling data pieces at the sampling positions “0” through “59” is 30 in the formulas above, the center is between “29” and “30” in a strict sense. Therefore, the formulas above may be as below: 
     
       
           AV (29)=( D (0)+ . . . + D (30)+ . . . + D (59))/60  
       
     
     (and so forth) 
     Thus calculated average values AV(X) are values from which the eccentric components of the roller  43  have been cancelled, and therefore, as the average values AV(X) are subtracted from the sampling data D(X), the eccentric components E(X) of the roller  43  at the respective sampling positions X are calculated. In other words, it is possible to calculate the eccentric components E(X) of the roller  43  by the following: 
     
       
           E ( X )= D ( X )− AV ( X )  
       
     
     (where X=30, 31, . . . 329) 
     Although this embodiment requires to obtain 360 pieces of the sampling data while rotating the roller  43  one more extra round than the number of rotation n (n=5) of the roller  43  which is needed for the intermediate transfer belt  41  to travel one round, and to thereafter calculate the eccentric components E(X) of the roller  43  based on these data pieces as described above, this may be modified to acquire  300  pieces of data while the roller  43  rotates n rounds (n=5) and to calculate the eccentric components E(X) of the roller  43  based on the 300 pieces of data. The fourth preferred embodiment, however, realizes a better effect as compared to the modification. Now, this will be described below. 
     Where data corresponding to only one round of the intermediate transfer belt  41  are sampled as in the modification, for calculation of eccentric components contained in one round of the belt, as shown in FIG. 17, it is necessary to supplement sampling data close to a rear end portion of the belt to calculation in the vicinity of a leading end portion of the belt and to supplement sampling data close to the leading end portion of the belt to calculation in the vicinity of the rear end portion of the belt. For this reason, the average values AV(X) and the eccentric components E(X) can be calculated only after the 300 pieces of data are stored in the memory  12 . Hence, the memory  12  needs be prepared to have a memory space to store the 300 pieces of sampling data. 
     In contrast, according to the fourth preferred embodiment, since the roller  43  rotates one more extra round, it is possible to calculate the first average value AV(X), and hence, the eccentric components E(X), immediately after acquiring 60 pieces of data since the start of data sampling. Further, the earliest data become unnecessary upon derivation of the eccentric components. This equally applies to the eccentric components at the subsequent sampling positions X, and therefore, a memory space which must be ensured in the memory  12  for the purpose of calculation only needs be large enough to hold 60 pieces of sampling data, which allows to reduce the memory size. In addition, this allows to execute the sampling operation and the calculation of eccentric components partially in parallel, and hence, to increase the overall processing speed. 
     Now, the sequence of measuring an actual quantity of toner will be described with reference to FIG.  18 . FIG. 18 is a flow chart showing a toner quantity measuring operation in the image forming apparatus shown in FIG. 1 (fourth preferred embodiment). In this apparatus, the control unit  1  executes steps (Step S 51  to Step S 55 ) similar to Step S 1  to Step S 5  which are used in the sequence of deriving the eccentric components, light quantity signal ratios (=SigP/SigS) which serve as an index regarding a toner quantity are calculated as the sampling data D(X) and stored in the memory  12 . 
     Next, at Step S 56 , the light quantity signal ratios obtained as described above are corrected using eccentric components E(x). The challenge at this stage is how to match the eccentric components E( 30 ), E( 31 ), . . . E( 329 ) obtained as described above with the data pieces D( 0 ), D( 1 ), . . . D( 299 ) sampled for toner quantity measurement, since after the data sampling for calculation of the eccentric components E(X) of the roller  43  (sampling A), the timing for starting data sampling for toner quantity measurement (sampling B) is not always constant, as shown in FIG.  19 . Noting this, the fourth preferred embodiment uses a different count value x to solve this problem, as shown in FIG.  19 . In short, after completing the data sampling A for calculation of eccentric components, cyclic counting processing is executed in which the count value x is incremented one at a time at intervals of 10 ms but returns to 30 once again upon reaching  329  while the roller  43  rotates. Hence, the count value x 0  upon sampling of the first piece of data D( 0 ) during the sampling B is a value between 30 and 329 which corresponds to a time interval AT until the start of the sampling B since the end of the sampling A. Therefore, regardless of the time interval ΔT, the eccentric components E(x) and the sampling data D(X) are appropriately associated with each other, which solves the problem above. 
     Every time the sampling data piece D(X) is obtained, the corresponding eccentric component E(x) is subtracted from the sampling data piece D(X). Hence, it is possible to correct the eccentric components of the roller by the formulas below: 
     
       
           D (0)− E ( x 0)  
       
     
     
       
           D (1)− E ( x 1)  
       
     
     
       
         . . .  
       
     
     
       
           D (299)− E ( x 299)  
       
     
     After this, the quantity of toner is measured based on the result of the correction (Step S 57 ). 
     As described above, according to the fourth preferred embodiment, since the eccentric components E(x) of the roller are calculated (Step S 46 ) and the sampling data D(X) obtained for measuring an actual quantity of toner are corrected using the eccentric components E(x) to thereby correct a change in sensing distance between the sensor  6  and the intermediate transfer belt  41  which is attributed to the eccentricity of the roller (Step S 56 ), it is possible to suppress an influence of the eccentricity of the roller and improve the measuring accuracy. 
     In addition, since this embodiment suppresses a change in distance (sensing distance) between the sensor  6  and the intermediate transfer belt  41 , it is possible to further improve the measuring accuracy as in the first preferred embodiment. 
     E. Fifth Preferred Embodiment 
     By the way, it is necessary to consider sampling intervals for more accurate measurement of a toner quantity, since when a belt cycle which an intermediate transfer belt  41  needs to run one round is a non-integer multiple of sampling intervals at which the CPU  11  samples the output voltages Vp and Vs, a phase difference is created between the rotation cycle of the intermediate transfer belt  41  and the sampling intervals. 
     When the belt cycle is an integer multiple of the sampling intervals, it is possible to measure a toner quantity at an excellent accuracy as described earlier even if the preferred embodiments above are executed as they are. Further, even when the belt cycle is a non-integer multiple of the sampling intervals, this is less influential if the phase difference is small to a negligible extent because of the short sampling intervals. However, for even more accurate measurement of a toner quantity by means of complete elimination of the phase difference, the eccentric components E(x) may be corrected an amount equivalent to the phase difference. A description will be now made on an application of the invention described above to an image forming apparatus in which the length of the circumference of the intermediate transfer belt  41  is a non-integer multiple of the length of the circumference of the sensor-facing roller  43  and the belt cycle is a non-integer multiple of the sampling intervals. 
     In an apparatus according to this embodiment, prior to measurement of a toner quantity, as shown in FIG. 20, as the predetermined period of time ΔT 1  elapses since outputting of the vertical synchronizing signal Vsync from the sensor  40 , sampling of the output voltages Vp and Vs is started. The output voltage Vp 0  upon turning off is then subtracted from the output voltage Vp at each sampling position x, thereby calculating the light quantity signal SigP (=Vp−Vp 0 ). In the meantime, the output voltage Vs 0  upon turning off is subtracted from the output voltage Vs at each sampling position x, thereby calculating the light quantity signal SigS (=Vs−Vs 0 ). The ratios of the light quantity signals (=SigP/SigS) are thereafter stored as the sampling data D(x) at the respective sampling positions x in a memory. Following this, in a manner similar to those in the preferred embodiments described earlier, the eccentric components E(x) and the periodic profile F(x) is calculated from this sampling data D(x). 
     For actual measurement of a toner quantity as well, as shown in FIG. 21, as the predetermined period of time elapses since outputting of the vertical synchronizing signal Vsync from the sensor  40 , sampling of the output voltages Vp and Vs is started and sampling data DD(x) for measurement are obtained. However, since the belt cycle P 41  is a non-integer multiple of the sampling intervals, sampling starts not after the predetermined period of time ΔT 1  but after a period of time ΔT 2  since outputting of the vertical synchronizing signal Vsync. In addition, the sensor-facing roller  43  is in different phases between upon calculation of the eccentric components E(x) and the periodic profile F(x) and upon detection for later calculation of a toner quantity. Thus, there are two types of displacement quantities in this embodiment. 
     In view of this, this embodiment requires to calculate these two types of displacement quantities in advance, and shift and correct the eccentric components E(x) calculated in the manner described above by these displacement quantities along the direction of time to thereby calculate the corrected eccentric components EE(x). This is followed by subtraction of eccentric components EE(x) and the periodic profile F(x) from the sampling data DD(x), whereby a correction value C(x) is calculated. A toner quantity is then measured based on the correction value C(x). 
     F. Others 
     The present invention is not limited to the preferred embodiments described above but may be modified in a variety of manners to the extent not departing from the spirit of the invention. For instance, although the sensor  6  is arranged to face the roller  43  in the preferred embodiments described above, the sensor  6  may be arranged to face the other rollers  42  and  44  to  47  around which the intermediate transfer belt  41  is stretched. However, since the roller  44  among the plurality of rollers  42  to  47  is a tension roller in the preferred embodiments described above, it is desirable that the sensor  6  is arranged to face one of these other rollers which are fixedly disposed to the main apparatus unit in advance so as to freely rotate at the fixed positions. This is because if the sensor  6  is arranged to face a roller which is fixedly disposed at a predetermined position for free rotation, a distance between this roller and the sensor  6  is constant. 
     On the other hand, since the tension roller  44  moves close to and away from the intermediate transfer belt  41 , a distance between the sensor  6  and the tension roller  44  tends to change. This changes a distance between the sensor  6  and the area of the belt in which the belt rests on the tension roller  44 , which is a cause of a deteriorated measurement accuracy. In order to prevent this, the tension roller  44  and the sensor  6  may be mechanically linked to each other so that as the tension roller  44  moves, the sensor  6  as well moves. 
     Further, although the preferred embodiments described above require to use the light quantity signal ratios (=SigP/SigS) which serve as an index regarding a toner quantity, other index value may be used such as the output voltages Vp and Vs, the light quantity signals SigP and SigS, the sum of the light quantity signals (=SigP+SigS) and a difference between the light quantity signals (=SigP−SigS). 
     Further, although the preferred embodiments described above use either (1) a structure that the sensor  6  is arranged facing the roller  43  to thereby suppress a change in sensing distance, (2) a structure that sampling data are corrected based on eccentric components of the roller, (3) a structure that sampling data are corrected based on a periodic profile (uneven thickness of the belt), or (4) a structure that sampling data are corrected based on a periodic profile (the condition of the surface of the belt), and eliminate influences of these factors to improve the accuracy of measuring the quantity of toner, it is needless to mention that the structures (1) through (4) may be used alone independently or appropriately combined with each other. 
     Further, although the light emitting element  601  and the light receiving elements  672   p  and  672   s  are arranged so that the surface of incidence receiving irradiated light and reflected light (the plane of FIG. 2) is approximately perpendicular to the axis of rotation of the sensor-facing roller  43  in the preferred embodiments described above as shown in FIG. 2, the relative arrangement of these elements is not limited to this. For example, the sensor  6  may be structured so that the surface of incidence mentioned above is approximately parallel to the axis of rotation of the roller. In addition, although the eccentricity of the roller changes the sensing distance and a change in angle of the roller surface (a surface of reflection) leads to a change in quantity of the reflected light if the surface of incidence is not parallel to the axis of rotation of the roller, with the surface of incidence positioned parallel to the axis of rotation of the roller, the angle of the surface of reflection becomes stable. Further, for the same reason, the surface of incidence and the axis of rotation of the roller may be arranged to be flush with each other for stabilizing the angle of the surface of reflection. 
     Further, although the present invention is applied to an image forming apparatus in which the intermediate transfer belt  41  is a belt-shaped image carrier according to the preferred embodiments described above, applications of the present invention are not limited to this. The present invention is also applied to an image forming apparatus in which a toner image is formed on a photosensitive belt. The present invention is generally applicable to image forming apparatuses which comprise a belt-shaped image carrier which is stretched across a plurality of rollers. 
     Further, although the preferred embodiments described above relate to an image forming apparatus which creates a color image using four toner colors, applications of the present invention are not limited to this. It is needless to mention that the present invention is applicable to an image forming apparatus which forms only a monochrome image. In addition, while the image forming apparatuses according to the preferred embodiments described above are printers which create an image supplied from an external apparatus, such as a host computer, on a sheet S such as a transfer paper, a copier paper and a transparency for an overhead projector, the present invention is generally applicable to image forming apparatuses of the electrophotographic type such as a copier machine and a facsimile machine. 
     Although the invention has been described with reference to specific embodiments, this description is not meant to be construed in a limiting sense. Various modifications of the disclosed embodiment, as well as other embodiments of the present invention, will become apparent to persons skilled in the art upon reference to the description of the invention. It is therefore contemplated that the appended claims will cover any such modifications or embodiments as fall within the true scope of the invention.