Patent Publication Number: US-9851672-B2

Title: Image forming apparatus that adjusts image forming conditions

Description:
BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention relates to an electrophotographic image forming apparatus that is used in devices such as copiers and printers. 
     Description of the Related Art 
     Image forming apparatuses employing an electrophotographic system or the like form an image pattern for tone correction on an intermediate transfer belt, detect the density of the image pattern, and perform tone correction based on the detected density. The surface wears with usage of the intermediate transfer belt, and unevenness occurs in the reflectance of the surface. This unevenness may also increase due to multilayering of a surface coat of the intermediate transfer belt. Since such unevenness affects the detected density of the image pattern, the accuracy of tone correction may be lowered. 
     U.S. Pat. No. 6,658,221 proposes creating a profile by sampling light reflected from the surface of an intermediate transfer belt on which a toner image is not formed, throughout one turn of the intermediate transfer belt, and using the profile to correct the detected density (amount of reflected light) of the image pattern. 
     Using the invention of U.S. Pat. No. 6,658,221 enables tone correction to be performed with high accuracy. However, the profile data for five turns of the intermediate transfer belt needs to be obtained. Since the user cannot form images during this period, so-called downtime occurs. A storage device for storing one turn worth of profile data is also required. 
     SUMMARY OF THE INVENTION 
     The present invention also reduces storage capacity together with reducing the time required for tone correction. 
     The present invention provides an image forming apparatus comprising the following elements. An image forming unit is configured to form an image. An intermediate transfer member is configured to have the image transferred thereto and to convey the image. A sensor is configured to measure light reflected from the intermediate transfer member. A controller is configured to control the image forming unit to form a measurement image, to control the sensor to measure light reflected from a first area of the intermediate transfer member, to control the sensor to measure light reflected from the measurement image, and to control the sensor to measure light reflected from a second area of the intermediate transfer member. A selection unit is configured to determine, from a plurality of measurement results of the first area, first information relating to a tendency of the measurement results of the first area, to determine, from a plurality of measurement results of the second area, second information relating to a tendency of the measurement results of the second area, and to select a computational equation for computing a correction value of a measurement result of the measurement image from among a plurality of computational equations, based on the first information and the second information. A generation unit is configured to generate the correction value from the measurement results of the first area and the measurement results of the second area, based on the computational equation selected by the selection unit. An adjustment unit is configured to adjust an image forming condition from the correction value generated by the generation unit and the measurement result of the measurement image. The first area corresponds to an area, on an upstream side of the measurement image in a conveyance direction in which the intermediate transfer member conveys the image, in which the measurement image is not formed. The second area corresponds to an area, on a downstream side of the measurement image in the conveyance direction, in which the measurement image is not formed. 
     Further features of the present invention will become apparent from the following description of exemplary embodiments (with reference to the attached drawings). 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is cross-sectional view of an image forming apparatus. 
         FIG. 2  is a block diagram of an image processing part. 
         FIG. 3  is a diagram showing a test image. 
         FIGS. 4A and 4B  are diagrams showing an example of a detection result. 
         FIG. 5A  is a block diagram of a tone control part. 
         FIG. 5B  is a block diagram of a correction part. 
         FIG. 6  is a flowchart showing processing for updating a look-up table. 
         FIG. 7  is a flowchart showing processing for updating a look-up table. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     Overall Configuration of Image Forming Apparatus 
       FIG. 1  is a schematic cross-sectional view of an image forming apparatus  100 . The image forming apparatus  100  is a copier that is able to form an image on a sheet (recording paper, OHT sheet, fabric, resin, etc.) using an electrophotographic system. The image forming apparatus  100  may also be a printer or a facsimile machine. 
     The image forming apparatus  100  has first, second, third and fourth image forming parts (stations) for respectively forming yellow (Y), magenta (M), cyan (C) and black (K) images, as image forming units that form toner images. The configurations of the image forming parts are the same except for the color of the toner that is used. Thus, reference signs have been given to only the image forming part  11  for yellow in  FIG. 1 . 
     In the image forming part  11 , a photosensitive drum  1 , which is a cylindrical photosensitive member, is provided as an image carrier. The photosensitive drum  1  rotates in the direction of an arrow R 1 . The surface of the photosensitive drum  1  is charged to a uniform potential by a charging roller  2  that serves as a charging unit. A laser beam scanner  3  that serves as an exposure unit irradiates the surface of the photosensitive drum  1  with a light beam that depends on image data, and forms an electrostatic latent image. A developing device  4  that serves as a developing unit develops the electrostatic latent image into a toner image (visible image) by adhering toner thereto. Primary transfer of the toner image is performed to an intermediate transfer belt  5  by a primary transfer roller  6 . The intermediate transfer belt  5  is an endless belt, and functions as an image carrier and the intermediate transfer member that carries and conveys the toner image. The intermediate transfer belt  5  rotates in the direction shown with an arrow R 2 . Secondary transfer of the toner image formed on the intermediate transfer belt  5  is performed to a sheet by secondary transfer rollers  7 . Toner remaining after the secondary transfer is removed from the surface of the intermediate transfer belt  5  by a cleaning apparatus  8  that serves as a cleaning unit. In the case where the cleaning apparatus  8  has a blade that removes toner by coming in contact with the surface of the intermediate transfer belt  5 , the surface of the intermediate transfer belt  5  gradually wears. This wear may cause unevenness of the reflectance of the surface of the intermediate transfer belt  5 . The toner image that has undergone secondary transfer to the sheet is fixed on the sheet by a fixing apparatus  9 . Note that the sheet may be referred to as a recording medium, a recording material, paper, transfer paper, a transfer material or a transfer medium. A sensor  10  is a sensor that detects the amount (optical density) of light reflected from the surface of the intermediate transfer belt  5 , and detects the amount (optical density) of light reflected from toner images formed on the surface of the intermediate transfer belt  5 . The sensor  10  has a light emitting element and a light receiving element. The light emitting element irradiates light toward the image carrier. Note that a mirror or the like may be included between the light emitting element and the image carrier. Types of reflected light include specularly reflected light and diffusely reflected light, and the sensor  10  is assumed to be disposed such that the light receiving element of the sensor  10  receives specularly reflected light. The sensor  10  may also be referred to as an optical sensor or a photo sensor. The sensor  10  thus functions as a measurement unit that irradiates light toward the image carrier and measures light reflected from the image carrier. 
     Image Processing Part 
     As shown in  FIG. 2 , an image processing part  20  is a unit that converts image data input from an image scanner or a host computer into image data for image formation. A color conversion part  21  converts the color space of input image data into the color space of the image forming part  11 . For example, input image data in RGB format or YUV format is converted into YMCK image data. A gamma part  22  is a unit that performs tone correction of the YMCK image data output from the color conversion part  21  in accordance with a tone correction condition. For example, the gamma part  22  uses a gamma look-up table, which is a tone correction condition set by a tone control part  23 , and corrects the tone properties of the input YMCK image data. Note that the gamma look-up table is a conversion condition for converting image data, and the gamma part  22  is an example of a conversion unit that converts image data based on the conversion condition. The tone correction condition is created in advance such that the tone properties of the input image data and the tone properties of the toner image formed on the sheet by the image forming apparatus  100  generally match. The tone properties of the original are thereby reproduced in the copy. The tone properties of the image forming part  11  change according to factors such as usage, ambient temperature, and the basis weight of the sheet. Thus, the gamma look-up table is updated or created according to these factors. The image forming part  11  is an example of an image forming unit that forms images based on the image data converted by the gamma part  22 . A halftone processing part  24  is a unit that binarizes the YMCK image data that is output from the gamma part  22 . The halftone processing part  24  binarizes the image data using processing such as dithering. The Y image data, the M image data, the C image data and the K image data output from the halftone processing part  24  are respectively supplied to corresponding laser beam scanners  3 . 
     Test Image 
     The tone control part  23  causes the image forming part  11  to create a toner image for tone correction (also referred to as a test image, image pattern, patch image or simply a patch), causes the sensor  10  to detect the toner image, and corrects the look-up table based on the detection result. In other words, the tone control part  23  creates, updates or corrects the look-up table so that the tone properties of the test image and the tone properties detected by the sensor  10  generally match. The tone properties may also be referred to as the density properties of the toner image. The tone control part  23  thus functions as a control unit that causes the image forming part  11  to form a measurement image on the image carrier, and causes the sensor  10  to measure light reflected from the image carrier on which the measurement image was formed. Furthermore, the tone control part  23  functions as a controller that causes the image forming unit to form a measurement image, causes the sensor  10  to measure light reflected from a first area of the intermediate transfer member, causes the sensor  10  to measure light reflected from the measurement image, and causes the sensor  10  to measure the light reflected from a second area of the intermediate transfer member. Such a function of controlling the image forming part  11  and the sensor  10  may be implemented in a controller that is external to the tone control part  23 , such as a CPU. 
       FIG. 3  shows an example of a test image  30  formed on the surface of the intermediate transfer belt  5 . The test image  30  is a toner image for performing tone correction and has a plurality of image patterns (patches) of respectively different tones, and the plurality of image patterns are formed on the surface of the intermediate transfer belt  5  at an interval from each other. According to  FIG. 3 , the test image  30  includes 10 patches of different tones for each of Y, M, C and K. In other words, 40 patches in total are formed on the surface of the intermediate transfer belt  5 . The shape of the patches is arbitrary, and here is a square of 20 mm×20 mm in size. In  FIG. 3 , three patches P 1 , P 2  and P 3  out of the 10 patches for yellow are shown. A non-image area, which is an area in which a toner image is not formed, is provided between each patch. For example, with regard to the patch P 1 , a non-image area B 0  adjacent on the downstream side in the movement direction (rotation direction) of the intermediate transfer belt  5  is secured, and a non-image area B 1  adjacent on the upstream side of the patch P 1  is secured. 
     An enlargement of the non-image area B 0 , the patch P 1  and the non-image area B 1  is also shown in  FIG. 3 . The amount of reflected light (also referred to as optical density) is detected by the sensor  10  at N positions (sampling points) for each of the non-image area B 0 , the patch P 1  and the non-image area B 1 . For example, the optical density is detected at sampling points Sp 0  to Sp 19  with regard to the non-image area B 0 . The optical density is detected at sampling points Sp 20  to Sp 39  with regard to the patch P 1 . The amount of reflected light and the optical density are correlated, and are thus interchangeable, and either may be used in the computations. 
     The sampling points may be absolute positions based on optical or magnetic marks (home positions) provided on the intermediate transfer belt  5 , or may be relative positions based on the write timing of the test image. The time from the write timing of the YMCK test images until the test images arrive at the detection position (measurement position) of the sensor  10  is a fixed value, and is known. Therefore, the sampling points can be managed using a counter or a timer. The present embodiment employs the latter, which enables a mechanism for detecting marks to be omitted. The tone control part  23  holds respective sampling points and sampled values (values of optical density detected by the sensor  10 ) in a memory or the like in association with each other. 
       FIGS. 4A and 4B  are figures showing an example of detection results for non-image areas and patches. The horizontal axis shows positions (sampling points) on the intermediate transfer belt  5 . The vertical axis shows values detected by the sensor  10 . In this example, the detected values for the patch P 1  are relatively low compared with the detected values for the non-image area B 0  and the non-image area B 1 . Note that this relationship differs according to differences in the material and color of the non-image areas and in the detection system (specularly reflected light detection system, diffusely reflected light detection system) of the sensor  10 . Note that, as above-mentioned, the influence of the reflectance of the non-image area where the patch P 1  is formed is included in the detected values of the patch P 1 . Since the reflectance of the non-image area changes due to factors such as the usage and soiling of the intermediate transfer belt  5 , the detected values of the patch P 1  needs to be corrected according to the state of the non-image areas. In particular, when a coating layer has been provided in the surface of the intermediate transfer belt  5 , light reflected from the surface of the coating layer interferes with light that passes through the coating layer and is reflected by the base substrate of the intermediate transfer belt  5 , and unevenness in the amount of reflected light in the non-image areas readily tends. 
     Although it is conceivable to detect the optical densities of the non-image areas throughout one turn of the intermediate transfer belt  5  and to hold the detected optical densities as a profile, problems such as discussed above arise in this case. In view of this, in the present embodiment, the tone control part  23  estimates the optical density (amount of reflected light) of the non-image area where the patch is formed using the detected value of the non-image area adjacent on the downstream side of the patch and the detected value of the non-image area adjacent on the upstream side. The tone control part  23  corrects the detected value for the patch using these estimated values. For example, the tone control part  23  reduces the influence of the reflected light of the non-image areas on the detected value of the specularly reflected light of the patch, by dividing the detected value of the optical density of the patch by the estimated value of the optical density of the non-image areas. When the detected value of a patch is given as LP i  (i is a variable) and the detected value (estimated value) of a non-image area where the patch is detected is given as LPB i , a corrected detected value SIG i  is calculated with the following equation (1). Note that LP i  may be the average value of detected values acquired at a plurality of sampling points (e.g.: 20 sampling points).
 
 SIG   i   =LP   i   /LPB   i   (1)
 
     Method of Estimating Optical Density of Non-Image Area and Method of Correcting Detected Value 
     The optical density of the non-image area where a patch is formed cannot be directly detected because of the patch. In view of this, the tone control part  23  may acquire the estimated value LPB i  of the optical density of the non-image area where an ith patch P 1  is formed based on the following equation (2).
 
 LPB   i =( LB   i-1   +LB   i )/2  (2)
 
     Here, LB i-1  is the detected value of the amount of reflected light of an i−1th non-image area. LB i  is the detected value of the optical density of an ith non-image area. As described above, an i−1th non-image area B i-1  is adjacent on the downstream side of the patch P i , and an ith non-image area B i  is adjacent on the upstream side of the patch P i . 
     If the sign of the gradient of the change in optical density of the i−1th non-image area B i-1  and the sign of the gradient of the change in optical density of the ith non-image area B i  are the same as shown in  FIG. 4A , the estimated value LPB i  of the optical density of the non-image area where the ith patch P i  is formed is accurately obtained, by using the equation (2). However, if, as shown in  FIG. 4B , the sign of the gradient of the change in optical density of the i−1th non-image area B i-1  and the sign of the gradient of the change in optical density of the ith non-image area B i  are not the same, the accuracy of the estimated value given by the equation (2) is low. Note that the gradients are the gradients of expressions f i-1 (x) and f i (x) of approximate straight lines that are obtained from a plurality of sampled values. x is a variable showing a position (sampling point). In view of this, in the present embodiment, the estimation method is switched based on the sign of the gradient of the change in optical density of the i−1th non-image area B i-1  and the sign of the gradient of the change in optical density of the ith non-image area B i . 
     Functions with which the tone control part  23  is provided and processing that the tone control part  23  executes will be described using  FIGS. 5A, 5B and 6 .  FIG. 5A  shows the functions with which the tone control part  23  is provided. The tone control part  23  may be realized by a CPU executing a program, or may be realized by an application-specific integrated circuit (ASIC) or a field-programmable gate array (FPGA).  FIG. 5B  shows the functions with which a correction part  55  is provided.  FIG. 6  shows steps that are executed by the tone control part  23 . The tone control part  23  is in charge of updating the above mentioned tone correction table (look-up table: LUT), and this update processing is also executable between sheets. This is because the optical densities of the non-image areas throughout one turn do not need to be obtained beforehand. Note that “between sheets” means the area between a preceding image and a following image on the intermediate transfer belt  5 , when forming a plurality of images continuously. 
     At step S 1 , a pattern generator  51  of the tone control part  23  reads out from a memory or creates image data for forming the test image  30 , and outputs the image data to the gamma part  22 . The gamma part  22  outputs the input image data to the halftone processing part  24  without modification. In accordance with the image data output from the halftone processing part  24 , the image forming part  11  forms the test image  30  on the intermediate transfer belt  5 . 
     At step S 2 , the tone control part  23  causes the sensor  10  to detect the optical density of each patch P i  of the test image  30  and the non-image areas B i-1  and B i  positioned before and after. The analog signal that is output by the light receiving element of the sensor  10  is converted into a digital value with an A/D converter, and input to the tone control part  23  as a detected value. Note that this digital value shows the amount of reflected light, and thus may be input to the tone control part  23  as a detected value after being converted into an optical density by a density conversion circuit or the like. A discarding part  52  is an optional unit, and may discard the detected value of one or more sampling points that are located near the boundary between the non-image areas B and the patch P, among the detected values of the plurality of sampling points. For example, the detected values of Sp 0 , Sp 1 , Sp 18  and Sp 19  may be discarded among the sampling points Sp 0  to Sp 19  of the non-image area B 0 . This is because the toner of the patch P may have splashed and adhered at such sampling points located near the boundary with the patch P, and these sampling points could possibly be affected by the toner. Note that the detected values for one or more sampling points (e.g.: Sp 20 , Sp 21 , Sp 38 , Sp 39 ) that are located near the boundary with the non-image areas B, among the detected values of the patch P, may also be discarded. 
     At step S 3 , an obtaining part  53  obtains the sign of the gradient of the change in optical density for the non-image area B i-1  on the downstream side of the ith patch P i  that is being focused on and the sign of the gradient of the change in optical density for the non-image area B i  on the upstream side. For example, the obtaining part  53  linearly approximates the detected values of the 16 sampling points Sp 2  to Sp 17  for the non-image area B i-1  on the downstream side, and acquires the linear expression f i-1 (x) and the gradient thereof. Similarly, the obtaining part  53  linearly approximates the detected values of the 16 sampling points Sp 42  to Sp 57  for the non-image area B i  on the upstream side, and acquires the linear expression f i (x) and the gradient thereof. The obtaining part  53  outputs the information on the gradients to a determination part  54 . The linear expressions f i (x) and (x) are passed to the correction part  55 . 
     At step S 4 , the determination part  54  determines whether the sign of the gradient for the non-image area B i-1  on the downstream side and the sign of the gradient for the non-image area B i  on the upstream side match. For example, the determination part  54  may multiply the gradient for the non-image area B i-1  on the downstream side and the gradient for the non-image area Bi on the upstream side to acquire the product thereof, and may determine whether both signs match or do not match depending on whether the sign of the product is positive or negative. Note that the case where both signs match is shown in  FIG. 4A , and the case where both signs do not match is shown in  FIG. 4B . The determination part  54  outputs the determination result to the correction part  55 . The correction part  55  advances the processing to step S 5  (first mode) if both signs match, and advances the processing to step S 8  (second mode) if both signs do not match. The correction part  55  thus functions as a selection unit that selects the computation mode of the correction value according to the gradients. Note that these gradients represent the state of the non-image area where the toner image is formed, and a correction value that depends on the state of the non-image area where the toner image is formed will be obtained by acquiring the correction value based on these gradients. More specifically, the correction part  55  functions as a selection unit that selects a mode that corresponds to a combination of the sign of the gradient of the optical density detected for the downstream area and the sign of the gradient of the optical density detected for the upstream area, from among a plurality of modes prepared in advance in order to determine the correction value for correcting the optical density for the toner image. This combination is the determination result of whether both signs match or not, and a mode that corresponds to this determination result or is suitable will be selected from among the plurality of modes. The determination result that the determination part  54  notifies to the correction part  55  will be information specifying or selecting a mode. Also, the correction part  55  functions as a selection unit that determines first information relating to a tendency of measurement results of a first area from a plurality of measurement results of the first area, determines second information relating to a tendency of measurement results of a second area from a plurality of measurement results of the second area, and selects a computational equation for computing a correction value of the measurement result of the measurement image from among a plurality of computational equations, based on the first information and the second information. The first area corresponds to an area in which a measurement image is not formed, on the upstream side of the measurement image in a conveyance direction in which the intermediate transfer member conveys an image. The second area corresponds to an area in which a measurement image is not formed, on the downstream side of the measurement image in the conveyance direction. 
     At step S 5 , the correction part  55  acquires a correction value in the first mode. In other words, a correction value computation part  64  of the correction part  55  functions as a determination unit that determines a correction value in accordance with the selected mode. The first mode is a mode in which the estimated value LPB i  of the optical densities of the non-image area where the ith patch P i  is formed is acquired with the estimation part  63  or the correction value computation part  64  using the above-mentioned equation (2), and LPB i  is employed as the correction value. Note that an averaging part  62  acquires an average value LB i-1  of Sp 0  to Sp 19  (or Sp 2  to Sp 17 ), and passes the average value to the estimation part  63  or the correction value computation part  64 . Similarly, the averaging part  62  acquires an average value LB i  of Sp 40  to Sp 59  (or Sp 42  to Sp 57 ), and passes the average value to the estimation part  63  or the correction value computation part  64 . The estimation part  63  or the correction value computation part  64  acquires an average value of the average value LB i-1  and the average value LB i , and outputs this average value to a division part  65  as the correction value LPB i . Also, the correction value computation part  64  functions as a generation unit that generates a correction value from the measurement results of the first area and the measurement results of the second area, based on a computational equation selected by the selection unit. 
     At step S 6 , the correction part  55  corrects the detected value LP i  of the ith patch P i  based on the correction value LPB i , and acquires the corrected detected value SIG i . For example, detected value LP 1  of the patch P 1  may be the average value of Sp 20  to Sp 39  (or Sp 22  to Sp 37 ) that is acquired with the averaging part  62 . The correction part  55  acquires the detected value SIG i  corrected using the equation (1), for example. In other words, the division part  65  may acquire the detected value SIG i  corrected by dividing the detected value LP i  by the correction value LPB i . The correction part  55  outputs the detected value SIG i  to the creation part  56 . Note that steps S 3  to S 6  are repeatedly executed for all of the patches for YMCK included in the test image  30 . In the case where 10 patches of respectively different tones exist for each of YMCK, the detected value SIG i  is created for 40 patches in total. 
     At step S 7 , the creation part  56  updates the look-up table (LUT) based on the detected value SIG i . As is well known, a look-up table for tone correction is a table for matching the tone properties of an input image and the tone properties of a toner image formed on a sheet. Therefore, the look-up table is created or updated such that the tone properties in the image data output from the pattern generator  51  and the tone properties acquired from the test image  30  match. For example, if the density (tone) in the image data of the patch P 1  is level 10 and the density acquired from the test image  30  is level 20, the look-up table is created so as to multiply the density of the input image data by 0.5. Also, for example, if the density in the image data of the patch P 1  is level 20 and the density acquired from the test image  30  is level 10, the look-up table is created so as to multiply the density of the input image data by 2. In other words, the look-up table is updated such that image data of level 5 is output when image data of level 10 is input, and image data of level 40 is output when image data of level 20 is input. If copying is executed using the updated look-up table, the toner image that is formed on a sheet will reproduce the tone of the original image. The look-up table thus is created or updated so as to have a function of reversing the ratio of the level of the input image data and the level of the output image data. Thus, the creation part  56  functions as an adjustment unit that adjusts the image forming conditions from the correction value generated by the generation unit and the measurement result of the measurement image. 
     When it is determined at step S 4  that the sign of the gradient for the non-image area on the downstream side and the sign of the gradient for the non-image area B i  on the upstream side do not match, the correction part  55  advances the processing to step S 8 . At step S 8 , the correction part  55  acquires a correction value in the second mode. In other words, the correction value computation part  64  of the correction part  55  functions as a generation unit that generates a correction value in accordance with the selected mode. 
     A method of acquiring a correction value in the second mode will be described with reference to  FIG. 4B . An intersection computation part  61  of the correction part  55 , based on the expressions f i-1 (x) and f i (x) of the approximate straight lines that are obtained by the obtaining part  53 , acquires coordinates (Spci, LPBci) of an intersection thereof. Furthermore, the estimation part  63  estimates an optical density LPBa i  of the non-image area at the downstream end (Sp 20  or Sp 22 ) of the patch P i  using the expression f i-1 (x) of the approximate straight line representing the optical density detected for the downstream area. In other words, the estimation part  63  acquires f i-1 (Sp 20 ) or f i-1 (Sp 22 ). The former is the value in the case where the discarding part  52  is not provided, and the latter is the value in the case where the discarding part  52  is provided. Furthermore, the estimation part  63  estimates an optical density LPBb i  of the non-image area at the upstream end (Sp 39  or Sp 37 ) of the patch P i  using the expression f i (x) of the approximate straight line representing the optical density detected for the upstream area. In other words, the estimation part  63  acquires f i (Sp 39 ) or f i (Sp 37 ). The former is the value in the case where the discarding part  52  is not provided, and the latter is the value in the case where the discarding part  52  is provided. The correction value computation part  64  acquires the correction value LPB i  based on LPBa i , LPBb i  and LPBc i . The correction value computation part  64  may acquire the correction value LPB i  based on the following equation (3), for example. Thereafter, the correction part  55  advances the processing to step S 6 .
 
 LPB   i =( LPBa   i   +LPBb   i   +LPBc   i )/3  (3)
 
     In the present embodiment, the optical density of a patch can thus be corrected according to the optical density of the non-image areas that are adjacent to the patch. Therefore, it is no longer necessary to create profiles of the optical densities of non-image areas throughout one turn, and the time required for tone correction is reduced. Since it is also not necessary to store profiles of the optical densities of non-image areas throughout one turn, the storage capacity of the memory required for correction is also reduced. Also, since tone correction is executable even between sheets, downtime of the image forming apparatus  100  is reduced. Also, since tone correction can be executed even when forming a plurality of images continuously, the tone reproduction of these plurality of images can be maintained with high accuracy. 
     In  FIG. 6 , the computation mode of the correction value was switched according to the sign of the gradient for the non-image area B i-1  on downstream side and the sign of the gradient for the non-image area B i  on the upstream side. However, as shown in  FIG. 7 , in the case where both signs do not match, step S 9  may be executed instead of step S 8 . As described above, in the case where both signs do not match, the accuracy of the correction value obtained using the equation (2) is low. In other words, it will likely be difficult to accurately reduce the influence of the amount of reflected light of the non-image areas that is included in the detected value of the patch even when this correction value is used. In view of this, by the discarding part  52  discarding all detected values for patches, or in other words, tone levels, with respect to which both signs do not match, these values may be excluded from the detected values for updating the look-up table. The discarding part  52  or the determination part  54  notifies the creation part  56  as to the detection values of what patches, or in other words, tone values, have been excluded. For example, when the detected value of a patch whose tone level is 10 is discarded, the creation part  56  does not perform updating of the portion for the patch whose tone level is 10 within the look-up table. In other words, the creation part  56  updates the look-up table partially, using the detected values that have not been discarded. Since the look-up table will be updated using only detected values having relatively high accuracy, an improvement in the accuracy of tone correction can be achieved. 
     SUMMARY 
     As described above, the intermediate transfer belt  5  is an example of an image carrier. The image forming part  11  is an example of an image forming unit that forms a toner image (test image  30 ) for performing tone correction on the intermediate transfer belt  5 . The sensor  10  functions as a detection unit that detects optical density. The above-mentioned LP, is the optical density of light reflected from the toner image formed on the intermediate transfer belt  5 . LB i-1  is the optical density of light reflected from a downstream area B i-1 , which is a non-image area, adjacent on the downstream side of the toner image in a rotation direction of the intermediate transfer belt  5 , in which a toner image is not formed. LB i  is the optical density of light reflected from an upstream area B i , which is a non-image area, adjacent on the upstream side of the toner image in the rotation direction, in which a toner image is not formed. The obtaining part  53  functions as an obtaining unit that obtains the gradient of the optical density detected for the downstream area and the gradient of the optical density detected for the upstream area. The correction part  55  functions as a correction unit that acquires a correction value that depends on the state of the non-image area where the toner image is formed based on the gradient of the optical density detected for the downstream area and the gradient of the optical density detected for the upstream area, and corrects the optical density for the toner image based on the correction value. The creation part  56  functions as a creation unit or an update unit that creates a tone correction condition that is based on the image data used in order to form the toner image and the optical density of the toner image corrected by the correction part  55 . In the present embodiment, the optical density of a patch can thus be corrected according to the optical density of the non-image areas that are adjacent to the patch. Thus, profiles of the optical densities of the non-image areas throughout one turn no longer need to be created, and the time required for tone correction is reduced. Since it is also not necessary to store profiles of the optical densities of the non-image areas throughout one turn, the storage capacity of the memory required for correction is also reduced. Also, since tone correction is executable even between sheets, the downtime of the image forming apparatus  100  is reduced. Also, since tone correction can be executed even when forming a plurality of images continuously, the tone reproduction of this plurality of images can be maintained with high accuracy. Note that the correction part  55  functions as a determination unit that determines a correction condition (e.g.: equation (2) or equation (3)) based on a first measurement result and a second measurement result. The first measurement result is a measurement result (e.g.: Sp 0 -Sp 19 ) corresponding to light reflected from a first area on the upstream side of the measurement image in a conveyance direction in which the image carrier conveys the measurement image. The second measurement result is a measurement result (e.g.: Sp 40 -Sp 59 ) corresponding to light reflected from a second area on the downstream side of the measurement image in the conveyance direction. The creation part  56  functions as a generation unit that generates a conversion condition, from the data included in the first measurement result, the data included in the second measurement result and the measurement result of the measurement image, based on the correction condition. Also, the correction part  55  may determine the correction condition according to the combination of the gradient of the optical density measured for the downstream area and the gradient of the optical density measured for the upstream area. The correction part  55  may be included in the creation part  56 . The correction part  55  determines the correction value for correcting the optical density of the measurement image using the data included in the first measurement result, the data included in the second measurement result, and the correction condition. Furthermore, the correction part  55  functions as a correction unit that corrects the optical density, which is a measurement result of the measurement image, using this correction value. The creation part  56  may generate the conversion condition based on the image data used in order to form the measurement image and the optical density of the measurement image corrected using the correction value. 
     As described using  FIG. 4A  and  FIG. 4B , the obtaining part  53  may linearly approximate the optical density from a plurality of positions in the downstream area and obtain the gradient of the optical density for the downstream area. Similarly, the obtaining part  53  may linearly approximate the optical density from a plurality of positions in the upstream area and obtain the gradient of the optical density for the upstream area. Also, the determination part  54  is an example of a determination unit that determines whether the sign of the gradient of the optical density for the downstream area and the sign of the gradient of the optical density for the upstream area are the same. 
     As described in relation to step S 5 , the averaging part  62  may acquire the average value of the optical density for the downstream area and the average value of the optical density for the upstream area, when the sign of the gradient of the optical density for the downstream area and the sign of the gradient of the optical density for the upstream area are the same. The estimation part  63  or the correction value computation part  64  functions as an estimation unit that estimates the optical density of the non-image area where the toner image is formed based on the average value of the optical density for the downstream area and the average value of the optical density for the upstream area. Also, the correction part  55  uses the optical density of the non-image areas estimated by the estimation part  63  or the correction value computation part  64  as the correction value. When the signs of both gradients thus match, the correction value will be acquired using a very simple computation. 
     As was described in relation to step S 8 , the correction part  55  may acquire the correction value using the second mode, when the sign of the gradient of the optical density for the downstream area and the sign of the gradient of the optical density for the upstream area are not the same. The intersection computation part  61  acquires the intersection of the approximate straight line representing the optical density detected for the downstream area and the approximate straight line representing the optical density detected for the upstream area. The estimation part  63  estimates the optical density of the non-image area at the downstream end of the toner image using the approximate straight line representing the optical density detected for the downstream area. Furthermore, the estimation part  63  estimates the optical density of the non-image area at the upstream end of the toner image using the approximate straight line representing the optical density detected for the upstream area. The intersection computation part  61  or the estimation part  63  estimates the optical density of the non-image areas at the intersection. The correction value computation part  64  acquires a correction value based on the optical density of the non-image area at the downstream end, the optical density of the non-image area at the upstream end, and the optical density of the non-image areas at the intersection. For example, the correction value computation part  64  may acquire the correction value using the equation (3). Thus, in the case where the accuracy of the correction value resulting from the equation (2) is low, the correction value may be acquired using the second mode. The accuracy of the correction value is thereby enhanced, and it becomes possible to update the look-up table accurately. In other words, an improvement in the accuracy of tone correction can also be achieved. 
     As described using the equation (3), the correction value computation part  64  may acquire the average value of the optical density of the non-image area at the downstream end, the optical density of the non-image area at the upstream end and the optical density of the non-image areas at the intersection, and the correction part  55  may use the average value as the correction value. It thereby becomes possible to accurately acquire the correction value by a comparatively simple computation, as compared with the equation (2), even in a case such as shown in  FIG. 4B . 
     As was described in relation to step S 9 , the creation part  56  does not need to perform updating of the tone correction condition based on the optical density of the toner image corrected by the correction part  55  when the sign of the gradient of the optical density for the downstream area and the sign of the gradient of the optical density for the upstream area are not the same. In other words, the creation part  56  does not need to reflect, in the tone correction condition, the optical density of patches, among the plurality of patches, with respect to which it is determined as the sign of the gradient of the optical density for the downstream area and the sign of the gradient of the optical density for the upstream area are not the same. On the other hand, the creation part  56  reflects, in the tone correction condition, the optical density of patches with respect to which it is determined that the sign of the gradient of the optical density for the downstream area and the sign of the gradient of the optical density for the upstream area are the same. Thus, the look-up table is partially updated with regard to patches (tone levels) with respect to which it is determined that both signs are the same, and the look-up table is not partially updated with regard to the patches (tone levels) with respect to which it is determined that both signs are not the same. By employing such partial updating, accurate updating of the look-up table can be achieved. 
     As was described in relation to step S 4 , the determination part  54  may use the product of the gradient of the optical density for the downstream area and the gradient of the optical density for the upstream area. The determination part  54  may determine whether the sign of the gradient of the optical density for the downstream area and the sign of the gradient of the optical density for the upstream area are the same according to whether the sign of this product is positive or negative. The sign determination may be realized using a simple computation such as this. 
     As was described in relation to step S 6 , the division part  65  of the correction part  55  may correct the optical density for the toner image by dividing the optical density for the toner image by the correction value. Correction of detected values may be realized by a simple computation such as this. Detected values may be corrected using more complex functions. 
     As described in relation to the gamma part  22 , the tone correction condition may be a tone correction table for correcting image data such that the tone of the image data and the tone of the toner image that is created using the image data are linear. Since such a tone correction table is often stored in the image forming apparatus  100  as a so-called look-up table, the present embodiment can be implemented in many image forming apparatuses. 
     As described using  FIG. 3 , the toner image for performing tone correction may have a plurality of image patterns of respectively different tones, and a plurality of image patterns may be formed on the surface of the image carrier at an interval from each other. Since non-image areas can thereby be secured on both sides of the patch, the present embodiment becomes easier to apply. 
     As described using  FIGS. 3, 4A  and the like, the discarding part  52  may discard detected values so as to not reflect at least the optical density detected at the nearest detection position to the toner image among the plurality of optical densities detected for the downstream area in the correction value. Similarly, the discarding part  52  may discard detected values so as to not reflect at least the optical density detected at the nearest detection position to the toner image among the plurality of optical densities detected for the upstream area in the correction value. This is because of the possibility of these non-image areas being affected by the splashing of toner from the patch. By not reflecting these optical density in the correction value, more accurate correction of the optical density of the patch can be possible. 
     The functions of the above-mentioned tone control part  23  may be executed by one processor, or the functions of the tone control part  23  may be executed by a plurality of processors. The functions of the discarding part  52 , the obtaining part  53 , the determination part  54 , the correction part  55  and the creation part  56  may respectively be executed by one processor, or the functions of the discarding part  52 , the obtaining part  53 , the determination part  54 , the correction part  55  and the creation part  56  may be executed by a plurality of processors. The functions of the intersection computation part  61 , the averaging part  62 , the estimation part  63 , the correction value computation part  64  and the division part  65  may respectively be executed by one processor, or the functions of the intersection computation part  61 , the averaging part  62 , the estimation part  63 , the correction value computation part  64  and the division part  65  may respectively be executed by a plurality of processors. 
     Also, the selection unit may be configured to generate first information relating to the change in light reflected from the first area based on first data and second data that are included in the plurality of measurement results of the first area, and to generate second information relating to the change in light reflected from the second area based on third data and fourth data that are included in the plurality of measurement results of the second area. The first data corresponds to the measurement result of light reflected from a first position that is included in the first area. The second data corresponds to the measurement result of light reflected from a second position included in the first area. The first position differs from the second position in the conveyance direction. The third data corresponds to the measurement result of light reflected from a third position included in the second area. The fourth data corresponds to the measurement result of light reflected from a fourth position included in the second area. The third position differs from the fourth position in the conveyance direction. 
     The plurality of computational equations may be also included in a first computational equation and a second computational equation. The first computational equation is a computational equation that calculates an average of the measurement result of the first area and the measurement result of the second area. The second computational equation is a computational equation that calculates a first approximate straight line based on the measurement result of the first area, calculates a second approximate straight line based on the measurement result of the second area, and calculates an average of the measurement result corresponding to the intersection of the first approximate straight line and the second approximate straight line, the measurement result of the first area and the measurement result of the second area. 
     The first information corresponds to the sign of the gradient of the first approximate straight line. The second information corresponds to the sign of the gradient of the second approximate straight line. If the sign of the gradient of the second approximate straight line and the sign of the gradient of the first approximate straight line are the same, the first computational equation is selected by the selection unit. If the sign of the gradient of the first approximate straight line and the sign of the gradient of the second approximate straight line are different, the second computational equation is selected by the selection unit. 
     The tone control part  23  is an example of a controller that causes an image forming unit to form a plurality of measurement images, causes a sensor to measure light reflected from a first area of the intermediate transfer member, causes a sensor to measure light reflected from the plurality of measured images, causes a sensor to measure light reflected from a second area of the intermediate transfer member, and causes a sensor to measure light reflected from a third area of the intermediate transfer member. The creation part  56  is an example of a generation unit that generates a tone correction condition based on the measurement result of the plurality of measurement images. The obtaining part  53 , the correction part  55  and the like are an example of an obtaining unit that determines first information relating to a tendency of the measurement result of the first area from a plurality of measurement results of the first area, determines second information relating to a tendency of the measurement result of the second area from a plurality of measurement results of the second area, and obtains third information relating to a tendency of the measurement result of the third area from a plurality of measurement results of the third area. The creation part  56  may control, based on the first information and the second information, whether a tone correction condition is generated based on the measurement result of a first measurement image formed between the first area and the second area, in a conveyance direction in which the intermediate transfer member conveys a plurality of measurement images. The creation part  56  may control, based on the second information and the third information, whether a tone correction condition is generated based on the measurement result of a second measurement image formed between the second area and the third area, in the conveyance direction. The first area corresponds to an area, on the upstream side of the first measurement image in a conveyance direction in which the intermediate transfer member conveys images, in which other measurement images included in the plurality of measurement images are not formed. The second area corresponds to an area, between the first measurement image and the second measurement image in the conveyance direction, in which other measurement images included in the plurality of measurement images are not formed. The third area corresponds to an area, on the downstream side of the second measurement image in the conveyance direction, in which other measurement images included in the plurality of measurement images are not formed. Also, the first information corresponds to the sign of the gradient of the first approximate straight line that is calculated from the measurement result of the first area. The second information corresponds to the sign of the gradient of the second approximate straight line that is calculated from the measurement result of the second area. The third information corresponds to the sign of the gradient of the third approximate straight line that is calculated from the measurement result of the third area. 
     The creation part  56  generates a tone correction condition, without using the first measurement image, in the case where the sign of the gradient of the first approximate straight line and the sign of the gradient of the second approximate straight line are different. The creation part  56  generates a tone correction condition, without using the second measurement image, in the case where the sign of the gradient of the second approximate straight line and the sign of the gradient of the third approximate straight line are different. The creation part  56  generates a tone correction condition based on the measurement result of the first measurement image and the measurement result of the second measurement image, in the case where the sign of the gradient of the first approximate straight line, the sign of the gradient of the second approximate straight line and the sign of the gradient of the third approximate straight line are the same. Note that the density of the first measurement image and the density of the second measurement image are different. 
     Other Embodiments 
     Embodiment(s) of the present invention can also be realized by a computer of a system or apparatus that reads out and executes computer executable instructions (e.g., one or more programs) recorded on a storage medium (which may also be referred to more fully as a ‘non-transitory computer-readable storage medium’) to perform the functions of one or more of the above-described embodiment(s) and/or that includes one or more circuits (e.g., application specific integrated circuit (ASIC)) for performing the functions of one or more of the above-described embodiment(s), and by a method performed by the computer of the system or apparatus by, for example, reading out and executing the computer executable instructions from the storage medium to perform the functions of one or more of the above-described embodiment(s) and/or controlling the one or more circuits to perform the functions of one or more of the above-described embodiment(s). The computer may comprise one or more processors (e.g., central processing unit (CPU), micro processing unit (MPU)) and may include a network of separate computers or separate processors to read out and execute the computer executable instructions. The computer executable instructions may be provided to the computer, for example, from a network or the storage medium. The storage medium may include, for example, one or more of a hard disk, a random-access memory (RAM), a read only memory (ROM), a storage of distributed computing systems, an optical disk (such as a compact disc (CD), digital versatile disc (DVD), or Blu-ray Disc (BD)™), a flash memory device, a memory card, and the like. 
     While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures and functions. 
     This application claims the benefit of Japanese Patent Application No. 2015-205839, filed Oct. 19, 2015 which is hereby incorporated by reference herein in its entirety.