Patent Publication Number: US-8983318-B2

Title: Image forming apparatus with a density sensor for detecting density fluctuations

Description:
TECHNICAL FIELD 
     The present invention relates to image forming apparatuses which form an image onto a medium such as paper, etc. 
     BACKGROUND ART 
     An image forming apparatus represented by a laser beam printer is known, wherein a light beam emitted from a light source is deflected and scanned in a main scanning direction by a deflecting and scanning unit, and is collected toward a drum (a photosensitive body) which has a face to be scanned, and a latent image is formed on a drum surface. In such an image forming apparatus, the latent image on the drum surface is transferred onto an intermediate transfer belt which is placed between the drum and a developing roller and an image which corresponds to the latent image is formed onto the intermediate transfer belt. 
     In the image which is formed onto the intermediate transfer belt, density fluctuations may occur in a main scanning direction and a sub-scanning direction, respectively. One possible cause of the density fluctuations is process gap (PG) fluctuations. First, the density fluctuations of the image in the main scanning direction are considered. As a factor for this, parallel characteristics of the drum (the photosensitive body) and the developing roller are possible. For example, when the mutual parallel characteristics of the drum and the developing roller are lost, variations occur in capabilities of developing onto the drum, possibly causing density fluctuations with respect to the main scanning direction. Here, the density fluctuations linearly change in the main scanning direction. 
     Next, the density fluctuations of the image in the sub-scanning direction are considered. One factor for this may be decentering of the drum. For example, when a slight movement of an axle of the drum occurs, positions at which a distance from a rotational axle of the drum to a surface differs occur, so that positions occur in which there is a difference in a gap between the drum and the developing roller. This difference in the gap becomes a developing variation, which would affect the image as the density fluctuations in the sub-scanning direction. 
     A different factor may be circularity of the drum. For example, assume that there is a second drum with low circularity relative to a first drum, which is circular. Then, with the second drum, at a time of rotation thereof, a difference occurs in a gap between the drum and the developing roller depending on a rotational angle, which may become a factor for fluctuations in developing. Due to the above-described factors, density fluctuations in the sub-scanning direction occur for an image formed on the drum surface. These density fluctuations become periodic, which occurs with a rotational period of the drum. 
     Factors for the density fluctuations include other factors such as potential variations of the drum, toner supply, toner removal, discharging, cleaning, etc., so that, combining them with density fluctuations due to process gap fluctuations, causes dynamic fluctuations to occur in both the main scanning direction and the sub-scanning direction. 
     In order to reduce such density fluctuations, for example, a light amount adjustment is performed in accordance with a transmitting characteristic of optics in the main scanning direction, for example. Moreover, for correcting in the sub-scanning direction, there is known a technique in which, for example, correction data are created in accordance with sensitivity variations of a photosensitive body to change a light amount in the sub-scanning direction, and a failure due to a phase offset of a rotational period of the photosensitive body and the correction data is avoided by an arithmetic calculation. 
     RELATED-ART DOCUMENTS 
     Patent Documents 
     Patent document 1: JP2008-065270A 
     Patent document 2: JP2003-127454A 
     However, besides the transmitting characteristics of the optics, there are density fluctuation producing factors in the main scanning direction, so that density fluctuations may occur in the main scanning direction over time. Moreover, there are also multiple density fluctuation producing factors in the sub-scanning direction, so that complex density fluctuations may occur by a combination thereof. With the above-described technique, a dynamic range of the density correction is narrow, so that it is difficult to realize a highly accurate density correction. 
     DISCLOSURE OF THE INVENTION 
     In light of the problems described above, an object of the present invention is to provide an image forming apparatus which makes it possible to improve a dynamic range of density correction and realize a highly accurate density correction. 
     According to an embodiment of the present invention, an image forming apparatus is provided. The image forming apparatus includes a light source; a drum which is a photosensitive body; an optical scanning apparatus which deflects and scans, in a main scanning direction by a deflecting and scanning unit, a light beam emitted from the light source, and collects, by a scanning and image forming unit, the deflected and scanned light beam on the drum, which drum has a face to be scanned, to form a latent image onto a surface of the drum; and an endless belt which is arranged to be in contact with the drum and on which an image corresponding to the latent image is formed, the image forming apparatus further including a pattern forming unit which forms, on the endless belt along a conveying direction of the endless belt, a density fluctuation detecting pattern having a period; a density sensor which detects the density fluctuating detecting pattern and outputs a density signal including information on density fluctuations in the conveying direction of the endless belt; and a period detecting sensor which detects the period included in the density fluctuations. 
     The disclosed technique makes it possible to provide an image forming apparatus which improves a dynamic range of density correction and which can realize a highly accurate density correction. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Other objects, features, and advantages of the present invention will become more apparent from the following detailed descriptions when read in conjunction with the accompanying drawings, in which: 
         FIG. 1A  is a schematic diagram exemplifying an image forming apparatus according to a first embodiment; 
         FIGS. 1B and 1C  are schematic diagrams exemplifying a density sensor; 
         FIG. 2A  is a diagram for describing a density fluctuation detecting pattern; 
         FIG. 2B  is a diagram for describing a method of density correction in a sub-scanning direction; 
         FIG. 3A  is a diagram illustrating a first part of a diagram for describing the method of density correction in a main scanning direction; 
         FIG. 3B  is a diagram illustrating a second part of the diagram for describing the method of density correction in the main scanning direction; 
         FIG. 3C  is a diagram illustrating a third part of the diagram for describing the method of density correction in the main scanning direction; 
         FIG. 4A  is a diagram illustrating a first part of a diagram for describing density calibration; 
         FIG. 4B  is a diagram illustrating a second part of the diagram for describing density calibration; 
         FIG. 5  is a diagram exemplifying a relationship between an image area rate and color difference fluctuations; 
         FIG. 6  is a diagram illustrating one example of a flowchart on density fluctuation correction according to the first embodiment; 
         FIG. 7  is a functional block diagram exemplifying a density fluctuation correcting unit according to the first embodiment; 
         FIG. 8  is a diagram exemplifying a density fluctuation detecting pattern according to a second embodiment; 
         FIG. 9  is a diagram exemplifying the image forming apparatus having multiple drums; 
         FIG. 10  is a diagram exemplifying the density fluctuation detecting pattern according to a third embodiment; 
         FIG. 11  is a schematic diagram exemplifying the image forming apparatus according to a comparative example; 
         FIG. 12  is a schematic diagram exemplifying the image forming apparatus according to a fourth embodiment; 
         FIG. 13  is a first part of a diagram for describing density calibration; 
         FIG. 14  is a second part of the diagram for describing density calibration; 
         FIG. 15  is a diagram for describing a method of density correction; 
         FIG. 16A  is a diagram for describing an example of density fluctuations in the sub-scanning direction according to drum circularity; 
         FIG. 16B  is another diagram for describing an example of density fluctuations in the sub-scanning direction according to the drum circularity; 
         FIG. 17  is a further diagram for describing an example of density fluctuations in the sub-scanning direction according to the drum circularity; 
         FIG. 18  is a diagram exemplifying a density fluctuation detecting pattern according to the fourth embodiment; 
         FIG. 19  is a diagram illustrating one example of a flowchart on density fluctuation correction according to the fourth embodiment; 
         FIG. 20  is a diagram exemplifying various signals related to density fluctuation correction according to the fourth embodiment; 
         FIG. 21  is a functional block diagram of a density fluctuation correcting unit according to the fourth embodiment; 
         FIGS. 22A to 22D  are diagrams exemplifying a behavior in the frequency domain of various signals shown in  FIG. 20 ; 
         FIG. 23  is a diagram exemplifying a density fluctuation detecting pattern according to a fifth embodiment; 
         FIG. 24  is a diagram exemplifying various signals related to density fluctuation correction according to the fifth embodiment; 
         FIG. 25  is a diagram exemplifying various signals related to density fluctuation correction according to a sixth embodiment; 
         FIG. 26  is a diagram illustrating a first part of a diagram exemplifying a density fluctuation detecting pattern according to a seventh embodiment; and 
         FIG. 27  is a diagram illustrating a second part of the diagram exemplifying the density fluctuation detecting pattern according to the seventh embodiment. 
     
    
    
     BEST MODE FOR CARRYING OUT THE INVENTION 
     A description is given below with regard to embodiments of the present invention with reference to the drawings. In the respective drawings, the same numbers are applied to the same elements, so that duplicate explanations may be omitted. 
     First Embodiment 
       FIG. 1A  is a schematic diagram exemplifying an image forming apparatus according to a first embodiment. With reference to  FIG. 1A , the image forming apparatus  10  includes an image processing unit  11 ; a light source driving apparatus  12 ; a light source  13 ; an optical scanning apparatus  15 ; a drum  16 ; an intermediate transfer belt  17 ; a density sensor  18 ; and a home position sensor  19  (which may be called an HP sensor  19  below). 
     In the image forming apparatus  10 , the density sensor  18  reads a density of a toner pattern formed onto the intermediate transfer belt  17 , and outputs, to the image processing unit  11 , a density signal V, which is an output signal in which an affixed amount of toner is converted to a voltage. For example, the density sensor  18  may be arranged such that a light emitted by an LED is irradiated onto the intermediate transfer belt  17  and a specularly reflected light and a diffuse reflected light which are obtained in accordance with a toner density on the intermediate transfer belt  17  is detected by a light receiving element. 
     The HP sensor  19 , which is a period detecting sensor which detects a rotational period of the drum  16 , outputs a home position signal W (which may be called an HP signal W below) to the image processing unit  11 . As described below, the image forming apparatus  10  may include multiple density sensors and multiple HP sensors. 
     The image processing unit  11  includes a CPU, a ROM, a RAM, a main memory, etc., for example, various functions of which image processing unit  11  may be realized by a program recorded in the ROM, etc., being read into the main memory to be executed by the CPU. A part or the whole of the image processing unit  11  may be realized by hardware only. Moreover, the image processing unit  11  may physically be configured with multiple apparatuses. 
     The image processing unit  11  detects density fluctuations based on an HP signal W and a density signal V input, calculates a light amount correction amount which corrects for the density fluctuations in the main scanning direction and the sub-scanning direction to generate and output, to the light source driving apparatus  12 , a light amount control signal A. The light source driving unit  12  drives the light source  13  based on the light amount control signal A. 
     As the light source  13 , a semiconductor laser, etc., may be used, for example. As a semiconductor laser, a VCSEL (Vertical Cavity Surface Emitting LASER), etc., may be used, for example. 
     A light beam emitted from the light source  13  is transmitted toward the drum  16 , which is a photosensitive body by the optical scanning apparatus  15 , and a latent image is formed onto a surface of the drum  16 . The optical scanning apparatus  15  includes, for example, a deflecting and scanning unit (not shown) which deflects and scans, in a main scanning direction, a light beam emitted from the light source  13 ; a scanning and image forming unit (not shown) which collects the deflected and scanned light beam onto the drum  16 , which is a face to be scanned, etc. 
     Then, after undergoing processes of developing and transferring, toner whose amount is based on a light emitting amount and a light emitting time of the light source  13  is affixed onto the intermediate transfer belt  17  and a predetermined image is formed. The intermediate transfer belt  17  is an endless belt which is arranged to be in contact with the drum  16  and onto which an image corresponding to the latent image is formed. 
     In this way, in the image forming apparatus  10 , light emitting level control of the light source  13  is performed with a light amount based on a light amount control signal A which corrects for density fluctuations in the main scanning direction and the sub-scanning direction. In this way, the respective density fluctuations in the main scanning direction and the sub-scanning direction may be decreased by control of a light amount of the light source  13 . 
     The light amount control signal A based on only density fluctuations in either one of the main scanning direction and the sub-scanning direction can also be generated to correct for only density fluctuations in the one of the main scanning direction and the sub-scanning direction. The main scanning direction is a direction which is orthogonal to a conveying direction of the intermediate transfer belt  17 , while the sub-scanning direction is the conveying direction of the intermediate transfer belt  17 . 
     Below main constituting elements of the image forming apparatus  10  are described in more detail.  FIGS. 1B and 1C  are schematic diagrams exemplifying a density sensor.  FIG. 1B  shows a case in which the toner is not affixed onto the intermediate transfer belt  17 , while  FIG. 1C  shows a case in which the toner is affixed onto the intermediate transfer belt  17 . 
     With reference to  FIGS. 1B and 1C , the density sensor  18  includes a light-emitting element  181 ; the specularly reflected light receiving element  182 ; and the diffuse reflected light receiving element  183 . The light emitting element  181  is a light emitting diode (LED), for example, while the specularly reflected light receiving element  182  and the diffuse reflected light receiving element  183  are photodiodes (PDs), for example. 
     As shown in  FIG. 1B , when the toner is not affixed onto the intermediate transfer belt  17 , a larger amount of light irradiated from the light emitting element  181  is represented by a light which is specularly reflected from the intermediate transfer belt  17 , and a larger amount of light is incident onto the specularly reflected light receiving element  182 . On the other hand, an amount of diffuse reflected light on the intermediate transfer belt  17  is small, so that almost no light is incident onto the diffuse reflected light receiving element  183 . 
     When the toner  50  is affixed onto the intermediate transfer belt  17  as shown in  FIG. 1C , an amount of the specularly reflected light becomes smaller, and an output signal of the specularly reflected light receiving element  182  becomes smaller. On the other hand, an amount of diffuse reflected light becomes larger, and an output signal of the diffuse reflected light receiving element  183  becomes larger. 
     In this way, for a case in which the toner  50  is not affixed and for a case in which the toner  50  is affixed, detected signal levels of the respective specularly reflected light receiving element  182  and diffuse reflected light receiving element  183  differ. This makes it possible to detect a density of the toner  50  on the intermediate transfer belt  17 . How the detected signal levels of the respective specularly reflected receiving element  182  and the diffuse reflected light receiving element  183  correspond to an actual image density cannot be discriminated only from the above-described configurations. This will be described below with reference to  FIGS. 4A and 4B . 
       FIG. 2A  is a diagram for describing a density fluctuation detecting pattern. As shown in  FIG. 2A , according to the present embodiment, a density fluctuation detecting pattern  20  for detecting density fluctuations is formed on the intermediate transfer belt  17  in synchronicity with an HP signal W which is detected with a rotation of the drum  16 . The density fluctuation detecting pattern  20  can be formed from a time which is delayed by Δt, for example, relative to the HP signal W to accurately detect density fluctuations at a specific location of the drum  16  by density sensors  18   a ,  18   b , and  18   c . Moreover, with the HP signal W as a trigger signal, a density signal which indicates density fluctuations can be repeatedly detected from the density fluctuation detecting pattern  20  by the density sensors  18   a ,  18   b , and  18   c  to obtain a more accurate density signal. 
       FIG. 2B  is a diagram for describing a method of density correction in the sub-scanning direction. With the HP signal W as a trigger signal, a density signal which indicates density fluctuations may be detected from the density fluctuation detecting pattern  20  by the density sensors  18   a ,  18   b , and  18   c . For example, a density signal Va with the same period as a period Td of the drum  16  may be detected from the density sensor  18   a.    
     Moreover, based on the density signal Va, as a correction signal Ha, a sinusoidal signal with a phase which is reverse that of the density signal Va and the same period as the period Td of the drum  16  may be generated. By controlling a light amount signal of the light source  13  using a correction signal Ha with a phase which is reverse that of the density signal Va, the density fluctuation detecting pattern can be formed to reduce density fluctuations of the formed density fluctuation detecting pattern in the sub-scanning direction, for example, see density signal Vx. 
     In other words, when the density fluctuation detecting pattern which is corrected for using the correction signal Ha is detected by the density sensor  18   a , for example, a signal whose amplitude is smaller than that of the density signal Va is obtained. In lieu of the density signal Va, which is an output signal of the density sensor  18   a , a correction signal may be generated based on an output signal of the density sensor  18   b  or  18   c  to reduce the density fluctuations in the sub-scanning direction. Moreover, a correction signal may be generated based on an average value of output signals of the density sensors  18   a  to  18   c  to reduce the density fluctuations in the sub-scanning direction. 
     In this way, a correction signal Ha which corrects for density fluctuations in the sub-scanning direction which is orthogonal to the main scanning direction may be generated based on an output signal of the HP sensor  19  and an output signal of at least one density sensor of multiple density sensors  18   a ,  18   b , and  18   c  which are arranged in parallel in the main scanning direction. Then, light emitting level control of the light source  13  may be performed with a light amount based on the correction signal Ha to reduce density fluctuations in the sub-scanning direction. The correction signal Ha does not have to be a sinusoidal periodic pattern, and may be set to be a triangular periodic pattern, a trapezoidal periodic pattern, etc., for example, in accordance with conditions. 
       FIG. 3A  is a diagram for describing a density correcting method in the main scanning direction. As shown in  FIG. 2A  as described above, when multiple density sensors (three density sensors  18   a ,  18   b , and  18   c  in this case) which are lined up in the main scanning direction are used to detect the density fluctuation detecting pattern  20 , in addition to the above-described periodic fluctuations in the sub-scanning direction, density signals Va, Vb, and Vc with differing signal levels are obtained in the main scanning direction as shown in  FIG. 3A . 
     Based on the HP signal W, the density signals Va, Vb, and Vc may be sampled for one period or for multiple periods to detect density fluctuations in the main scanning direction as shown in  FIG. 3B . As shown in  FIG. 3C , density fluctuations in the main scanning direction can be reduced by linearly interpolating density signals Va, Vb, and Vc to generate the interpolated signal Sx, reversing the interpolated signal Sx to generate a correction signal Hb, and controlling a light amount signal of the light source  13  using the correction signal Hb. 
     While the above explanations have been given by breaking down into the sub-scanning direction and the main scanning direction for convenience, in practice, the correction signal Ha in the sub-scanning direction and the correction signal Hb in the main scanning direction are independently generated, and a light amount control signal A (see  FIG. 1A ) in which the correction signal Ha and the correction signal Hb are convolved is generated to drive the light source  13 . In this way, the respective density fluctuations in the main scanning direction and the sub-scanning direction may be reduced by control of a light amount of the light source  13 . 
       FIGS. 4A and 4B  are drawings for describing density calibration. In order to perform density correction, it is necessary to know a fluctuating amount of density relative to light amount fluctuations. As shown in  FIG. 4A , a case is considered of successively increasing an amount of light which forms a pattern by control of an exposure power of the light source  13 , drawing a density calibrating pattern  25  which has 11 levels (11 types) of rectangular-shaped patterns with differing densities in the sub-scanning direction, and detecting, by the density sensor  18   a  on the sub-scanning line, density signal V (including V 1  to V 11 ) which correspond to the respective patterns which make up the density calibrating pattern  25 .  FIG. 4A  shows that a light amount is caused to be changed in intervals of 2% from −10% to +10% relative to a reference light amount. 
     Then, between the respective patterns which make up the density calibrating pattern  25  and the light amount increased for changing the density, there is a generally linear relationship. Moreover, there is also a generally linear relationship between the density of the respective patterns which make up the density calibrating pattern  25  and the density signal V (including V 1  to V 11 ), a generally linear relational data between the light amount and the density signal V (including V 1  to V 11 ) may be obtained as shown in  FIG. 4B . 
     Furthermore, an actual print may be performed to measure an image density with a colorimeter, a scanner, etc., and a correspondence thereof with the density signal V (including V 1  to V 11 ) may be made to take a correlation between an actual image density and the density signal V (including V 1  to V 11 ). Similarly, for the density sensors  18   b  and  18   c , a correlation may be taken between the actual image density and the density signal. 
     While an example is shown in  FIG. 4A  of forming the density calibrating pattern  25  with 11 levels of exposure power that are changed by controlling exposure power of the light source  13 , the density calibrating pattern  25  may be formed with at least 3 levels of exposure power that are changed by controlling exposure power of the light source  13  to calculate a change amount of the density relative to light amount fluctuations of the light source  13 . 
     In the present embodiment, the image area rates of the density fluctuation detecting pattern  20  shown in  FIG. 2A  and the density calibrating pattern  25  shown in  FIG. 4A  are respectively set between 50% and 85%. When correcting for density fluctuations within a page, correction can be performed favorably by changing a color difference in increments of 0.2 from a point of sensing by a density sensor or visual inspection. When the image area rate is between 50% and 85%, color difference fluctuations on paper becomes approximately 4 when the light amount is changed +10% as shown in  FIG. 5 . Therefore, in order to change the color difference in increments of 0.2, it suffices that a light amount control resolution be ±0.5%. 
     On the other hand, when the image area rate is other than between 50% and 85%, in order to change the color difference in increments of 0.2, the light amount control resolution becomes approximately ±1%, so that a dynamic range of density correction becomes narrow when taking into account upper and lower limits of a light amount change. The image area rate is a numerical value which indicates how much of a basic matrix of a dot or a parallel line is occupied when outputting a certain density pattern, and may also be called a dot area rate. For example, for a checker-shaped density pattern, the image area rate becomes 50%. The image area rate on paper may be calculated by calculating backwards from a CCD or a spectroscope. 
     In this way, setting the image area rate of the density fluctuation detecting pattern  20  between 50% to 85% causes a dynamic range of density correction to be wide, so that accurate density fluctuation data for density correction can be obtained for density fluctuations caused by the drum  16 , making it possible to realize an image forming apparatus  10  which can reduce density fluctuations in a simple configuration. The same applies also to the density calibrating pattern  25 . 
     Here, density fluctuation correction is described in further detail below with reference to  FIGS. 6 and 7 .  FIG. 6  is an example of a flowchart on density fluctuation correction according to the first embodiment.  FIG. 7  is a functional block diagram exemplifying a density fluctuation correcting unit according to the first embodiment. A calibrating unit  30   a , a pattern forming unit  30   b , and a correcting signal generating unit  30   c  of the density fluctuation correcting unit  30  shown in  FIG. 7  may be realized by the image processing unit  11 , the light source driving apparatus  12 , the light source  13 , the optical scanning apparatus  15 , etc. 
     With reference to  FIGS. 6 and 7 , first in step S 401 , the calibrating unit  30   a  forms a density calibrating pattern as shown in  FIG. 4 , for example, at a position corresponding to the density sensors  18   a ,  18   b , and  18   c  on the intermediate transfer belt  17 . Then, the calibrating unit  30   a  forms a uniform density calibrating pattern with at least three levels (11 levels in the example in  FIG. 4A ) of exposure power that are changed by control of exposure power in the light source  13  and with the image area rate between 50% and 85%. Next, in step S 403 , the calibrating unit  30   a  obtains a density signal of the respective density sensors  18   a ,  18   b , and  18   c  which correspond to the density calibrating pattern  25 . 
     Next, in step S 405 , the calibrating unit  30   a  obtains correlation data between the respective density signal levels and light emitting power (light amount) of the light source  13  as shown in  FIG. 4B , for example, and saves it in a memory, etc. In this way, correlation is taken between the density calibrating pattern  25  and the respective density signals obtained from the density sensors  18   a ,  18   b , and  18   c . In other words, a correspondence between amplitude of the density signals and a density of an image formed onto the intermediate transfer belt is identified, making it possible to discriminate a magnitude of the density relative to the density signal (the density is calibrated). 
     Next, in step S 407 , the pattern forming unit  30   b  forms a density fluctuation detecting pattern  20  as shown in  FIG. 2A , for example, at a position which corresponds to the density sensors  18   a ,  18   b , and  18   c  that are on the intermediate transfer belt  17  with a rotational period of the drum  16  that is detected by the HP sensor  19 . Then, the pattern forming unit  30   b  forms a uniform density fluctuation detecting pattern  20  with an image area rate between 50% and 85%. 
     Next, in step S 409 , the correction signal generating unit  30   c  obtains the respective density signals (density signals Va, Vb, and Vc, which are indicated in  FIG. 3A ) of the density sensors  18   a ,  18   b , and  18   c  that correspond to the density fluctuation detecting pattern  20 . Next, in step S 411 , the correction signal generating signal  30   c  generates a periodic pattern corresponding to density fluctuations in the sub-scanning direction. The periodic pattern corresponding to the density fluctuation in the sub-scanning direction may be obtained by approximating a signal in which density signals Va, Vb, Vc shown in  FIG. 3A  are averaged with a sinusoidal wave. Alternatively, the periodic pattern corresponding to the density fluctuations in the sub-scanning direction may be obtained by approximating, with a sinusoidal wave, an output signal of at least one density sensor, out of the density signals Va, Vb, and Vc shown in  FIG. 3A . 
     Next, in step S 413 , the correction signal generating unit  30   c  generates a correction signal which is a sinusoidal signal with a phase which is reverse that of a periodic pattern corresponding to the density fluctuations in the sub-scanning direction. Next, in step S 415 , the correction signal generating unit  30   c  causes a correction signal pattern generated in step S 413  to, for example, undergo an A/D conversion to save the converted pattern in the memory, etc. Only a periodic pattern of a correction signal that corresponds to one period may be saved as a basic pattern. 
     Next, in step S 417 , the correction signal generating unit  30   c  obtains an average value (see  FIG. 3B , for example) for each density sensor for the respective density signals (density signals Va, Vb, and Vc shown in  FIG. 3A , for example) of the density sensors  18   a ,  18   b , and  18   c  that correspond to the density fluctuation detecting pattern  20 . 
     Next, in step S 419 , the correction signal generating unit  30   c  generates an approximation formula (a formula which shows a pattern of an interpolation signal Sx shown in  FIG. 3C , for example) corresponding to the density fluctuations in the main scanning direction. Next, in step S 421 , the correction signal generating unit  30   c  generates a light emitting power correction formula (for example, a formula which shows a pattern of the correction signal Hb in  FIG. 3C ) for correcting the density fluctuations in the main scanning direction. Next, in step S 423 , the correction signal generating unit  30   c  saves, in the memory, etc., a light emitting power correction formula generated in step S 421 . 
     Thereafter, based on the light emitting power correction formula saved in step S 423  and the correction signal pattern saved in step S 415 , the correction signal generating unit  30   c  generates a light amount control signal A in which both are convolved, and performs light emitting level control of the light source  13  with a light amount based on the light amount control signal A. In this way, the respective density fluctuations in the main scanning direction and the sub-scanning direction may be reduced by control of a light amount of the light source  13 . In other words, a density fluctuation correction is performed with a method in  FIG. 6  to obtain a high quality image on the intermediate transfer belt  17 , in which image, density fluctuations in the main scanning direction and the sub-scanning direction are reduced. 
     In this way, setting an image area rate of the density fluctuation detecting pattern between 50% and 85% causes a wide dynamic range of density correction, so that accurate density fluctuation data for density fluctuation correction can be obtained for density fluctuations caused by the drum, making it possible to realize the correction with a simple configuration. 
     Second Embodiment 
     In a second embodiment, an example of a density fluctuation detecting pattern which is different from the first embodiment is shown.  FIG. 8  is a diagram exemplifying a density fluctuation detecting pattern according to the second embodiment. With reference to  FIG. 8 , the density fluctuation detecting patterns  20   a ,  20   b , and  20   c  with a sub-scanning direction for detecting density fluctuations as a longitudinal direction are arranged immediately below the density sensors  18   a ,  18   b , and  18   c  which are arranged in multiple numbers in the main scanning direction. 
     The density fluctuation detecting patterns  20   a ,  20   b , and  20   c  can be formed to suppress an amount of consumption of toner with an advantageous effect equivalent to that of the density fluctuation detecting pattern  20  shown in  FIG. 2A . 
     Third Embodiment 
     According to a third embodiment is shown an example in which the present invention is applied to a tandem color machine which includes multiple photosensitive bodies.  FIG. 9  is a diagram exemplifying an image forming apparatus including multiple drums (photosensitive bodies). With reference to  FIG. 9 , the image forming apparatus  40 , which includes a configuration in which optical scanning apparatuses  45   a ,  45   b ,  45   c , and  45   d  corresponding to the colors of cyan, magenta, yellow, and black, for example, along the intermediate transfer belt  17 , which is an endless belt, is a so-called tandem-type image forming apparatus. The intermediate transfer belt  17  is an endless belt which is wound around various rollers which are rotationally driven. 
     The optical scanning apparatuses  45   a ,  45   b ,  45   c , and  45   d , which respectively include light sources (not shown), direct light beams emitted from the light sources to the respective drums  16   a ,  16   b ,  16   c , and  16   d  via a deflector (not shown) and multiple optical components (not shown) and form a latent image on the respective drums  16   a ,  16   b ,  16   c , and  16   d.    
     In the vicinity of the drums  16   a ,  16   b ,  16   c , and  16   d  are arranged HP sensors  19   a ,  19   b ,  19   c , and  19   d , respectively. Functions of the HP sensors  19   a ,  19   b ,  19   c , and  19   d  are the same as those of the HP sensor  19  which were described in the first embodiment. 
     In the image forming apparatus  40 , the rotational timing or period may differ somewhat for each of the drums  16   a ,  16   b ,  16   c , and  16   d . In other words, for the image forming apparatus  40 , a drum differs for each of colors of cyan, magenta, yellow, and black, so that timings for generating an HP signal for each drum also differs. Thus, when density fluctuation detecting pattern of each color is generated onto the intermediate transfer belt  17 , a density detecting pattern is generated in response to a timing of an HP signal which differs from color to color. In this way, from an aspect of image quality, an image with good color reproducibility in which density fluctuations for each of the drums  16   a ,  16   b ,  16   c , and  16   d  are effectively reduced is obtained. 
       FIG. 10  is a diagram exemplifying a density fluctuation detecting pattern according to a third embodiment. In  FIG. 10 , density fluctuation detecting patterns  21   a ,  21   b , and  21   c  which are formed in parallel in the main scanning direction are cyan patterns; density fluctuation detecting patterns  22   a ,  22   b , and  22   c  which are formed in parallel in the main scanning direction are magenta patterns; density fluctuation detecting patterns  23   a ,  23   b , and  23   c  which are formed in parallel in the main scanning direction are yellow patterns; and density fluctuation detecting patterns  24   a ,  24   b , and  24   c  which are formed in parallel in the main scanning direction are black patterns. 
     Moreover, in  FIG. 10 , an HP signal Wc is an output signal from the HP sensor  19   a  corresponding to cyan; an HP signal Wm is an output signal from the HP sensor  19   b  corresponding to magenta; an HP signal Wy is an output signal from the HP sensor  19   c  corresponding to yellow; and an HP signal Wb is an output signal from the HP sensor  19   d  corresponding to black. 
     In  FIG. 10 , the cyan density fluctuation detecting patterns  21   a ,  21   b , and  21   c  corresponding to two periods of the HP signal Wc are generated; then, at a different position in the sub-scanning direction, the magenta density fluctuation detecting patterns  22   a ,  22   b , and  22   c  corresponding to two periods of the HP signal Wm are generated; then, at a different position in the sub-scanning direction, the yellow density fluctuation detecting patterns  23   a ,  23   b , and  23   c  corresponding to two periods of the HP signal Wy are generated; and then, at a different position in the sub-scanning direction, the black density fluctuation detecting patterns  24   a ,  24   b , and  24   c  corresponding to two periods of the HP signal Wb are generated. 
     The reason that the density fluctuation detecting pattern corresponding to two periods of the respective HP signals is generated is that there may a case in which an S/N ratio is small at a time of detecting by a density sensor with only a density fluctuation detecting pattern corresponding to one period of the respective HP signals. Therefore, in order to increase an S/N ratio when detecting by the density sensor, a density fluctuation detecting pattern corresponding to at least three periods of the respective HP signals may be formed. 
     A density fluctuation detecting pattern formed that corresponds to multiple periods of the respective HP signals may be detected by each density sensor and an average processing may be performed among signals at the same position to more accurately detect periodic density fluctuations which are caused by a drum shape, etc. Therefore, a correction signal may be generated based on the density signal and a light amount of a light source may be controlled to realize an apparatus which forms an image with a high image quality in which density fluctuations are reduced. 
     Fourth Embodiment 
     First, in describing an image forming apparatus according to a fourth embodiment, a related-art image forming apparatus as a comparative example is described.  FIG. 11  is a schematic diagram exemplifying the image forming apparatus according to the comparative example. With reference to  FIG. 11 , an image forming apparatus  100  according to a comparative example includes an image processing ASIC  11 ; a light source driving apparatus  13 ; a light source  14 ; an optical scanning apparatus  15 ; a drum  16 ; an intermediate transfer belt  17 ; and a density sensor  18 . 
     In  FIG. 11 , a light amount control signal A (main shading data) which is output from the image processing ASIC  11  is a light amount control signal in a main scanning direction (rotational axle direction) of the drum  16 . The optical control signal A is input to the light source driving apparatus  13 , which drives the light source  14  with a light amount based on the light amount control signal A and performs light emitting level control of the light source  14  (controls exposure power of the light source  14 ). As the light source  14 , a semiconductor laser, etc., may be used, for example. As a semiconductor laser, a VCSEL (Vertical Cavity Surface Emitting LASER), etc., may be used, for example. 
     A light beam emitted from the light source  14  is transmitted toward the drum  16 , which is a photosensitive body, by the optical scanning apparatus  15 , and a latent image is formed on a surface of the drum  16 . The optical scanning apparatus  15  includes, for example, a deflecting and scanning unit (not shown) which deflects and scans, in the main scanning direction, the light beam emitted from the light source  14 ; a scanning and image forming unit (not shown) which collects the deflected and scanned light beam onto the drum  16 , which is a face to be scanned, etc. 
     Then, after undergoing processes of developing and transferring, a toner whose amount is based on a light emitting amount and a light emitting time of the light source  14  is affixed onto the intermediate transfer belt  17  and a predetermined image is formed. The intermediate transfer belt  17  is an endless belt which is arranged to be in contact with the drum  16  and onto which an image corresponding to the latent image is formed. 
     The density sensor  18  reads a density of a toner pattern formed onto the intermediate transfer belt  17 , and outputs, to the image processing ASIC  11 , a density signal V, which is an output signal in which an affixed amount of toner is converted to a voltage. For example, the density sensor  18  may be arranged such that a light emitted by an LED is irradiated onto the intermediate transfer belt  17  and a specularly reflected light and a diffuse reflected light which are obtained in accordance with a toner density on the intermediate transfer belt  17  is detected by a light receiving element. 
       FIG. 12  is a schematic diagram exemplifying an image forming apparatus according to the fourth embodiment. With reference to  FIG. 12 , the image forming apparatus  10  is different from the image forming apparatus  100  (see  FIG. 11 ) in that a shading data converting unit  12  and a home position sensor  19  (which may be called a HP sensor  19  below) are added. The image forming apparatus  10  not only corrects for shading in the main scanning direction as in the image forming apparatus  100 , but also corrects shading in the sub-scanning direction. 
     In the image forming apparatus  10 , a light amount control signal A (main shading data) output from the image processing ASIC  11 , a density signal V which is output from the density sensor  18 , and a home position signal W (which may be called an HP signal W below) which is output from the HP sensor  19  are respectively input to the shading data converting unit  12 . The HP sensor  19  is a period detecting sensor which detects a rotational period of the drum  16 . 
     The shading data converting unit  12  includes a function of generating sub-shading data which corrects for shading in the sub-scanning direction as a signal which is synchronized to the HP signal W, etc. Moreover, it includes a function of multiplying the generated sub-shading data with the light amount control signal A (main shading data) to generate a light amount control signal B (main shading data+ sub-shading data). 
     The shading data converting unit  12  includes a CPU, a ROM, a main memory, etc., for example, various functions of which shading data converting unit  12  are realized by a program recorded in the ROM, etc., being read into the main memory to be executed by the CPU. A part or the whole of the shading data converting unit  12  may be realized by hardware only. Moreover, the shading data converting unit  12  may physically be configured with multiple apparatuses. 
     The light amount control signal B is input to the light source driving apparatus  13 , which controls a light emitting level of the light source  14  with a light amount based on the light amount control signal B. In this way, the respective density fluctuations in the main scanning direction and the sub-scanning direction may be decreased by control of a light amount of the light source  14 . It is also possible to control the light source  14  based on only sub-shading data, not combining the generated sub-shading data with the light amount control signal A (the main shading data), and correct for shading only in the sub-scanning direction. The main scanning direction is a direction which is orthogonal to a conveying direction of the intermediate transfer belt  17 , while the sub-scanning direction is the conveying direction of the intermediate transfer belt  17 . 
       FIGS. 13 and 14  are diagrams for describing density calibration. As shown in  FIG. 13 , a case is considered of successively increasing an amount of light for forming a pattern; drawing, in the sub-scanning direction, a density calibrating pattern  20  which includes ten rectangular-shaped patterns with differing densities; and detecting, by the density sensor  18  on the sub-scanning line, a density signal V (including V 1  to V 10 ) which corresponds to the respective patterns which makes up the density calibrating pattern  20 . 
     Then, between the respective patterns which make up the density calibrating pattern  20  and the light amount increased for changing the density, there is a generally linear relationship. Moreover, there is also a generally linear relationship between the density in the respective patterns which make up the density calibrating pattern  20  and the density signal V (including V 1  to V 10 ), and generally linear relational data between the light amount and the density signal V (including V 1  to V 10 ) may be obtained as shown in  FIG. 14 . Moreover, an actual print may be performed to measure an image density with a colorimeter, a scanner, etc., and a correspondence thereof with the density signal V (including V 1  to V 10 ) may be made to take a correlation between an actual image density and the density signal V (including V 1  to V 10 ). 
       FIG. 15  is a diagram for describing a density correction method. For example, a case is considered of forming a certain density pattern in multiple numbers within a time width of a period T 1  of the drum  16 . 
     Here, a period T 1  in a drum  16  is not necessarily equivalent to a print size, and a print starting position relative to the drum  16  is not constant. As density fluctuations of the drum  16  with a period T 1  occur, with an HP signal W as a trigger, an HP sensor  19  may be provided to specify the period T 1  of the drum  16 . 
     A phase and the period T 1  of the drum  16  are specified by the HP sensor  19  to obtain a density signal Va, which is close to a sinusoidal wave with the same period as the period T 1  of the drum  16  from the density sensor  18 . Based on density fluctuations of the density signal Va, as a correction signal Y, a sinusoidal signal with a phase which is reverse that of a density fluctuation Va and the same period as a period T 1  of the drum  16  may be generated. Amplitude of the sinusoidal signal becomes a correction amount. 
     Forming the density fluctuation detecting pattern by inputting, into the light source driving apparatus  13 , a correction signal Y with a phase which is reverse that of the density fluctuation Va to control a light amount of the light source  14  makes it possible to reduce density fluctuations of the formed density fluctuation detecting pattern in the sub-scanning direction. In other words, when the density fluctuation detecting pattern which is formed using the correction signal Y is detected by the density sensor  18 , a signal whose amplitude is smaller than that of the density signal Va, such as a density signal Vb, is obtained. In the density signal Vb, a density fluctuating component with the period T 1  of the drum  16  is reduced relative to the density signal Va. 
     While not shown in  FIG. 12 , in practice, as shown in  FIGS. 16A ,  16 B, and  FIG. 17 , a developing roller  22 , which is a rotating body, is located at a position opposing the drum  16 , between which an intermediate transfer belt  17  (not shown) is placed. In other words, with the intermediate transfer belt  17  being placed between the drum  16  and the developing roller  22 , rotating of the drum  16  and the developing roller  22  in a predetermined direction causes the intermediate transfer belt  17  to be conveyed in the sub-scanning direction. The developing roller  22  includes a function of developing a latent image which is formed onto the drum  16 . 
     Then, the HP sensor  19  includes an HP sensor  19   a  which detects a home position of the drum  16  and an HP sensor  19   b  which detects a home position of the developing roller  22 . The HP sensor  19   a  is a first period detecting sensor which detects density fluctuations of a period T 1  which corresponds to rotating of the drum  16 , while the HP sensor  19   b  is a second period detecting sensor which detects density fluctuations of a period T 2  which corresponds to rotating of the developing roller  22  which is different from a rotational period of the drum  16 . The HP sensor  19   a  outputs an HP signal W 1  to the shading data converting unit  12 , while the HP sensor  19   b  outputs an HP signal W 2  to the shading data converting unit  12 . The period T 1  is one representative example of the first period according to the present invention, while the period T 2  is one representative example of the second period according to the present invention. 
     With reference to  FIGS. 16A ,  16 B, and  17 , an example is described of density fluctuations in the sub-scanning direction due to the circularity of the drum  16 . An image density varies depending on a gap between the drum  16  and the developing roller  22 . As shown in  FIG. 16A , when the drum  16  is circular, the image density stabilizes to a certain value as shown in a broken line (a) in  FIG. 17 . On the other hand, as shown in  FIG. 16B , when the circularity of the drum  16  is low, a gap fluctuation occurs due to a rotational position as shown in solid and broken lines of the drum  16 , so that the image density also changes with rotating of the drum  16 . 
     In  FIG. 16B , there are two fluctuating portions with a diameter which is larger and with a diameter which is smaller relative to a circle, so that as shown with a solid line (b) in  FIG. 17 , a density of an image corresponding to one period (T 1 ) of the drum  16  appears as a density fluctuation which is close to a sinusoidal wave having two inflection points. Therefore, it is desirable to generate around at least five locations of density fluctuation detecting patterns as shown in black circles in  FIG. 17  between output signals of the HP sensor  19   a  that corresponds to one period of the drum  16  to detect density fluctuations. 
       FIG. 18  is a diagram exemplifying a density fluctuation detecting pattern according to the fourth embodiment. With reference to  FIG. 18 , for density fluctuation detection, on the intermediate transfer belt  17  are formed density fluctuation detecting patterns  23  and  24  at different positions in the vertical direction (the main scanning direction) relative to the conveying direction of the intermediate transfer belt  17  (rotating direction of the drum  16 ). The respective density fluctuation detecting patterns  23  and  24 , which are shown in  FIG. 18 , are representative examples of the first density fluctuation detecting pattern and the second density fluctuation detecting pattern according to the present invention. 
     The density fluctuation detecting pattern  23 , which is a pattern formed in synchronicity with the HP signal W 1  which is detected with rotating of the drum  16 , has a first occurrence period. While the first occurrence period is set to six patterns within a period T 1  of the HP signal W 1  in an example in  FIG. 18 , it is not limited thereto. 
     Moreover, the density fluctuation detecting pattern  24 , which is a pattern formed in synchronicity with the HP signal W 2  which is detected with rotating of the developing roller  22 , has a second occurrence period which is different from the first occurrence period. While the second occurrence period is set to five patterns within a period T 2  of the HP signal W 2  in an example in  FIG. 18 , it is not limited thereto. A pattern interval of the density fluctuation detecting pattern  24  may be set to be a constant interval for a multiple number of periods of the period T 2 . 
     The density fluctuation detecting pattern  23  is generated from a time which is delayed by Δt1, for example, relative to a rise of the HP signal W 1  of period T 1  (from tb0 to tb1) while the density fluctuation detecting pattern  24  can be generated from a time which is delayed by Δt2, for example, relative to a rise of the HP signal W 2  of period T 2 . 
     Now, with reference to  FIGS. 19 to 21 , a density fluctuation correction using the density fluctuation detecting patterns  23  and  24  which are shown in  FIG. 18  is described.  FIG. 19  is an example of a flowchart on density fluctuation correction according to the fourth embodiment.  FIG. 20  is a diagram exemplifying various signals related to density fluctuation correction according to the fourth embodiment.  FIG. 21  is a functional block diagram of a density fluctuation correcting unit  30  according to the fourth embodiment. 
     A calibrating unit  30   d , a first pattern forming unit  30   e , a second pattern forming unit  30   f , a first correction signal generating unit  30   g , and a second correction signal generating unit  30   h  which are shown in  FIG. 21  may be realized by the shading data converting unit  12 , the light source driving unit  13 , the light source  14 , the optical scanning apparatus  15 , etc. 
     With reference to  FIGS. 19 to 21 , first, in step S 101 , the calibrating unit  30   d  forms two columns of density calibrating patterns  20  having 10 rectangular patterns with differing densities as shown in  FIG. 13 , for example, at a position (in the sub-scanning direction) corresponding to density sensors  18   a  and  18   b  on the intermediate transfer belt  17 . Next, in step S 102 , the density sensors  18   a  and  18   b  respectively detect density signals from the density calibrating patterns  20  of the two columns. 
     Next, in step S 103 , the calibrating unit  30   d  obtains correlation data between the density signal and density calibrating pattern  20  of each column as shown in  FIG. 14 , for example. In this way, a correlation is taken between the density signals obtained from the density sensors  18   a  and  18   b  and the density calibrating pattern  20  of each column. In other words, a correspondence between amplitude of a density signal and a density of an image formed onto the intermediate transfer belt  17  is identified, making it possible to discriminate a magnitude of the density relative to the density signal. 
     Next, in step S 104 , the first pattern forming unit  30   e  forms the density fluctuation detecting pattern  23  (a first density fluctuation detecting pattern) as shown in  FIG. 18 , for example, in a position corresponding to the density sensor  18   a  on the intermediate transfer belt  17  along a conveying direction of the intermediate transfer belt  17 . Next, in step S 105 , the density sensor  18   a  detects a density fluctuation detecting pattern  23  and outputs a first density signal X 11  as shown in  FIG. 20 , for example. The first density signal X 11  is a signal which includes information on density fluctuations in a conveying direction of the intermediate transfer belt  17 . 
     Next, in step S 106 , the first correction signal generating unit  30   g  generates a first correction signal Y 11  (a signal with a period T 1  and a frequency f 1 ), which is a sinusoidal signal with a phase which is reverse that of density fluctuations as shown in  FIG. 20 , for example, based on a first density signal X 11 . Next, in step S 107 , the first correction signal generating unit  30   g  causes a value of the first correction signal Y 11  generated in step S 106  to undergo A/D conversion, for example, to hold the converted result in a memory (not shown), etc. 
     Next, in step S 108 , the second pattern forming unit  30   f  inputs the first correction signal Y 11  in the light source driving apparatus  13  to control a light amount of the light source  14  to form a density fluctuation detecting pattern  24  (a second density fluctuation detecting pattern). Next, in step S 109 , the density sensor  18   b  detects the density fluctuation detecting pattern  24  and outputs a second density signal X 12  as shown in  FIG. 20 , for example. The second density signal X 12  is a signal which includes information on density fluctuations in the conveying direction of the intermediate transfer belt  17 . 
     Next, in step S 110 , the second correction signal generating unit  30   h  generates a second correction signal Y 12  (a signal with a period T 2  and a frequency f 2 ), which is a sinusoidal signal with a phase which is reverse that of density fluctuations as shown in  FIG. 20 , for example, based on a second density signal X 12 . Next, in step S 111 , the second correction signal generating unit  30   h  causes a value of the second correction signal Y 12  generated in step S 110  to undergo A/D conversion, for example, to hold the converted result in a memory (not shown), etc. 
     Thereafter, the second correction signal Y 12 , which is held in the memory (not shown), etc., may be input into the light source driving apparatus  13  to control a light amount signal of the light source  14  to form a density fluctuation detecting pattern in which density fluctuations with periods T 1  and T 2  are reduced. When the density fluctuation detecting pattern, which is corrected with the second correction signal Y 12 , is detected with a density sensor, a third density signal X 13  is formed in which density fluctuations with periods T 1  and T 2  are reduced relative to the first density signal X 11  and the second density signal X 12  as shown in  FIG. 20 , for example. In other words, a density fluctuation correction is performed with a method in  FIG. 19  to obtain an image with a high image quality on the intermediate transfer belt  17 , in which image density fluctuations with the period T 1  and period T 2  are reduced. 
     While an example of performing a density correction only with sub-shading data (the second correction signal Y 12 ) is shown, in practice, the sub-shading data (the second correction signal Y 12 ) are multiplied with a light amount control signal A (main shading data) to generate a light amount control signal B (main shading data+ sub-shading data). Then, the light amount control signal B may be input to the light source driving apparatus  13  to control a light amount signal of the light source  14  to reduce the respective density fluctuations in the main scanning direction and the sub-scanning direction by a light control amount of the light source  14 . 
       FIG. 22A to 22D  are diagrams exemplifying a behavior in the frequency domain of various signals shown in  FIG. 20 . In  FIG. 22A to 22D , the horizontal axis shows frequency, while the vertical axis shows a signal level.  FIG. 22A  shows a frequency distribution of the first density signal X 11  shown in  FIG. 20 . As shown in  FIG. 22A , for the first density signal X 11  is seen a frequency distribution with a frequency f 1  and a frequency f 2  as centers, which frequency f 1  corresponds to a period T 1 , which is a rotational period of the drum  16 , which frequency f 2  corresponds to a period T 2 , which is a rotational period of the developing roller  22 . 
       FIG. 22B  shows respective frequency distributions of the first correction signal Y 11  and the second correction signal Y 12  shown in  FIG. 20 . The first correction signal Y 11  and the second correction signal Y 12  are respectively generated as sinusoidal signals, so that, as shown in  FIG. 22B , they indicate frequency distributions of only a frequency f 1  which corresponds to a period T 1  and a frequency f 2  which corresponds to a period T 2 . 
       FIG. 22C  shows a frequency distribution of the second density signal X 12  shown in  FIG. 20 . As shown in  FIG. 22C , in the second density signal X 12 , the first density signal X 11  is already corrected for with the first correction signal Y 11 , so that, in comparison to  FIG. 22A , a frequency component with a frequency f 1  as a center decreases and only a frequency component with a frequency f 2  as a center appears prominently. 
       FIG. 22D  shows a frequency distribution of the third density signal X 13  shown in  FIG. 20 . As shown in  FIG. 22D , in the third density signal X 13 , a frequency component with the frequency f 2  as a center decreases in comparison to  FIG. 22C  since the second density signal X 12  is already corrected for with the second correction signal Y 12 . In other words, compared to  FIG. 22A , frequency components with the frequency f 1  and the frequency f 2  decrease. 
     In this way, frequency components of both the frequency f 1  which corresponds to the period T 1 , which is a rotational period of the drum  16 , and the frequency f 2  which corresponds to the period T 2 , which is a rotational period of the developing roller  22 , may be corrected for dynamically to reduce density fluctuations which occur periodically. In other words, for density fluctuations which occur due to fluctuations in a physical position between the drum  16  and the developing roller  22 , accurate density signals for density fluctuation correction can be obtained, so that an image forming apparatus which can reduce density fluctuations may be realized in a simple configuration. 
     Moreover, as the density fluctuation detecting patterns which detect two signals are generated simultaneously, a one time density detecting time becomes shorter in comparison to a case in which the density fluctuation detecting patterns for detecting two types of periodic signals that correspond to different home position signals are generated, so that a waiting time, etc. is reduced. 
     Fifth Embodiment 
     In a fifth embodiment, an example is shown of detecting the density fluctuation detecting patterns  23  and  24  by one density sensor. 
       FIG. 23  is a diagram exemplifying a density fluctuation detecting pattern according to the fifth embodiment.  FIG. 24  is a diagram exemplifying various signals related to the density fluctuation correction according to the fifth embodiment. With reference to  FIG. 23 , on the intermediate transfer belt  17 , the density fluctuation detecting patterns  23  and  24  for detecting density fluctuations are formed on the same straight line relative to a conveying direction of the intermediate transfer belt  17  such that a part of each overlaps the other. According to the fifth embodiment, the density fluctuation detecting patterns  23  and  24  are detected by only one density sensor  18 . 
     In the density fluctuation correction according to the fifth embodiment, steps S 101  to S 107  in  FIG. 19  are exactly the same as in the density fluctuation correction according to the fourth embodiment. In step S 108 , it is different from the fourth embodiment in that the density fluctuation detecting pattern  24  is formed on the same straight line relative to a conveying direction of the intermediate transfer belt  17  such that it overlaps a part of the density fluctuation detecting pattern  23 . 
     In step S 109 , unlike in the fourth embodiment, one density sensor  18  simultaneously detects the density fluctuation detecting patterns  23  and  24  formed such that a part of each overlaps the other, so that a density signal X 21  as shown in  FIG. 24 , for example, is output. The density signal X 21  is a signal which includes information on density fluctuations in a conveying direction of the intermediate transfer belt  17 . 
     Here, when the period T 1  of the HP signal W 1 &gt; the period T 2  of the HP signal W 2  (when the frequency f 1  of the HP signal W 1 &lt; the frequency f 2  of the HP signal W 2 ), as seen from the density signal X 21 , it is difficult to discriminate the density fluctuation with the period T 2 . 
     Then, the first correction signal generating unit  30   d  generates a correction signal Y 21  (frequency f 1 ) by causing data shown with a circle for the density signal X 21  (data corresponding to the density fluctuation detecting pattern  23 ) to undergo an FFT (fast Fourier transform), etc. Then, the correction signal Y 21  is multiplied by the density signal X 21  to obtain a second density signal X 22 , in which density fluctuations with the period T 1  are reduced. In the obtained second density signal X 22 , a density fluctuation component of a period T 1  is reduced, so that a tendency of density fluctuations with the period T 2  appears. 
     Next, in step S 110 , the second correction signal generating unit  30   e  generates a second correction signal Y 22  (a signal with a period T 2  and a frequency f 2 ), which is a sinusoidal signal with a phase which is reverse that of density fluctuations as shown in  FIG. 24 , for example, based on a second density signal X 22 . Next, in step S 111 , the second correction signal generating unit  30   e  causes a value of the second correction signal Y 22  generated in step S 110  to undergo A/D conversion, for example, to hold the converted result in a memory (not shown), etc. 
     Thereafter, the second correction signal Y 22 , which is held in the memory (not shown), etc., may be input into the light source driving apparatus  13  to control a light amount signal of the light source  14  to form density fluctuation detecting patterns in which density fluctuations with periods T 1  and T 2  are reduced. When the density fluctuation detecting pattern which is corrected for with the second correction signal Y 22  is detected by the density sensor, a third density signal X 23  is obtained in which density fluctuations with periods T 1  and T 2  are reduced as shown in  FIG. 24 . In other words, a density fluctuation correction is performed with a method in  FIG. 19  to obtain a high quality image on the intermediate transfer belt  17 , in which image density fluctuations with the period T 1  and period T 2  are reduced. 
     In this way, in the fifth embodiment, the same advantages are yielded as in the fourth embodiment; as one density sensor  18  detects density fluctuation detecting patterns  23  and  24 , which are formed such that a part of each pattern overlaps the other, a number of parts of the density sensor in the image forming apparatus may be reduced, contributing to a decreased cost. 
     Sixth Embodiment 
     In the sixth embodiment, an example is shown of detecting the density fluctuation detecting patterns  24  only by one density sensor. 
     In the density fluctuation correction according to the sixth embodiment, steps S 101  to S 103  in  FIG. 19  are exactly the same as in the density fluctuation correction according to the fourth embodiment. In step S 104 , the second pattern forming unit  30   c  forms a density fluctuation detecting pattern  24  (a second density fluctuation detecting pattern) as shown in  FIG. 18 , for example, in a position corresponding to the density sensor  18   a  on the intermediate transfer belt  17  along a conveying direction of the intermediate transfer belt  17 . 
     Next, in step S 105 , the density sensor  18  detects a density fluctuation detecting pattern  24  and outputs a density signal X 31 , which is synchronized to the period T 2  of the HP signal W 2  as shown in  FIG. 25 , for example. The density signal X 31  is a signal which includes information on density fluctuations with periods T 1  and T 2  in the conveying direction of the intermediate transfer belt  17 . Here, the first correction signal generating unit  30   d  samples a number of points in the density signal X 31  at predetermined timings and generates a first density signal X 32  corresponding to the HP signal W 1  from the sampled signal. 
     Next, in step S 106 , the first correction signal generating unit  30   d  generates a first correction signal Y 31  (a signal with a period T 1  and a frequency f 1 ), which is a sinusoidal signal with a phase which is reverse that of density fluctuations as shown in  FIG. 25 , for example, based on a first density signal X 32 . Next, in step S 107 , the first correction signal generating unit  30   d  causes a value of the first correction signal Y 31  generated in step S 106  to undergo A/D conversion, for example, to hold the converted result in a memory (not shown), etc. Next, the same process as in steps S 108 -S 111  according to the fourth embodiment is executed. In this way, the same advantageous effect as in the fourth embodiment is obtained. 
     The HP signal W 2  relative to the HP signal W 1  is a non-synchronous signal, so that, a delay time of, for example, Δtd1, occurs for the density fluctuation detecting pattern  24  for which writing is started at a timing of the HP signal W 2  relative to the HP signal W 1 . Then, the delay time of Δt12 between the HP signal W 1  and the HP signal W 2  may be detected to calculate a timing, relative to the HP signal W 1 , at which writing of the density fluctuation detecting pattern  24  is started. Thus, a phase difference of the density fluctuation signals may be detected, making it possible to accurately calculate density fluctuations with the period T 1  of the HP signal W 1 . 
     In this way, even a method of forming only the density fluctuation detecting pattern  24  corresponding to a shorter period T 2  twice may be used to reduce density fluctuations with periods T 1  and T 2 . 
     Moreover, multiple density detections may be performed with one density fluctuation detecting pattern without a need to have multiple types of density fluctuation detecting patterns to realize a reduced size and cost of circuitry in the image forming apparatus. 
     Seventh Embodiment 
     In a seventh embodiment, an example is shown of forming a set of density fluctuation detecting patterns  23  and  24  in multiple numbers. 
       FIG. 26  is a first part of a diagram exemplifying a density fluctuation detecting pattern according to the seventh embodiment. With reference to  FIG. 26 , on the intermediate transfer belt  17 , sets of density fluctuation detecting patterns  23  and  24  shown in  FIG. 18  are formed in multiple numbers at different positions in the vertical direction (the main scanning direction) relative to the conveying direction of the intermediate transfer belt  17 . Moreover, the density sensors  18   a  to  18   f  are arranged at positions corresponding to the respective density fluctuation detecting patterns. 
     In this way, the sets of density fluctuation detecting patterns  23  and  24  are formed in multiple numbers at different positions in the vertical direction (the main scanning direction) relative to the conveying direction of the intermediate transfer belt  17  to obtain density signals by the corresponding density sensors, so that information on density fluctuations within a face in one round of the developing roller  22  and the drum  16  is obtained. As a result, an average value of density fluctuation detecting signals obtained at multiple positions in the main scanning direction on the intermediate transfer belt  17  may be taken, etc., to obtain information on average density fluctuations within the face and also to realize accurate density fluctuation detection and density fluctuation correction. 
       FIG. 27  is a second part of the diagram exemplifying the density fluctuation detecting pattern according to the seventh embodiment. As shown in  FIG. 27 , sets of density fluctuation detecting patterns  23  and  24  shown in  FIG. 23  may be formed in multiple numbers at different positions in the orthogonal direction (the main scanning direction) relative to the conveying direction of the intermediate transfer belt  17 , while arranging density sensors  18   a - 18   c  at positions corresponding to the density fluctuation detecting patterns. Even in this way, the same advantageous effect as in  FIG. 26  is obtained. 
     While preferred embodiments have been described in the above in detail, they are not limited to the above-described embodiments, so that various changes and modifications may be added to the above-described embodiments without departing from the scope recited in the claims. 
     For example, for an image forming apparatus having multiple developing rollers, an HP sensor corresponding to a drum and multiple HP sensors corresponding to each of the multiple developing rollers may be used to perform density correction. In other words, n HP sensors may be used to correct for density fluctuations with n periods. 
     Moreover, in lieu of a method of changing a light amount of a light source as a scheme of correcting for density fluctuations, a method of changing a developing bias of the developing roller, etc., may be used. 
     The present application is based on Japanese Priority Applications No. 2012-061245 and 2012-061246, which were filed on Mar. 16, 2012, the entire contents of which are hereby incorporated by reference.