JP2014026059A - Image forming apparatus - Google Patents

Abstract

PROBLEM TO BE SOLVED: To improve correction accuracy of density unevenness in an image forming apparatus.SOLUTION: Each image forming unit 10Y, 10M, 10C and 10K of an image forming apparatus 1 includes a photoreceptor drum 11 rotating in a direction of an arrow A, a charger 12 charging the photoreceptor drum 11, a laser exposing device 13 writing an electrostatic latent image on the photoreceptor drum 11, and a developing device 14 housing a toner of each color component and visualizing the electrostatic latent image on the photoreceptor drum 11 with the toner. An image formation control unit 50 includes a density correction value storage memory 80 that stores a density correction value for correcting density unevenness so as to suppress the density unevenness in an image to be formed, and the image formation control unit 50 controls an operation of each section. The density correction value is a value at a corresponding portion where a set portion preliminarily set on a transfer target material on which an image is to be formed, is actually output on the transfer target material.

Description

  The present invention relates to an image forming apparatus.

  As a prior art described in the publication, Patent Document 1 discloses a belt-like image extending in the main scanning direction and having a predetermined density, and a correction reference position set in units of a predetermined number of pixels in the main scanning direction on the belt-like image. And an auxiliary line extending in the sub-scanning direction, and a control unit that generates a correction image, and an image that forms the correction image generated by the control unit on a sheet and outputs a correction chart A forming unit; an input unit for inputting a correction value of the density of the pixel at the correction reference position based on the correction chart; and a correction value input by the input unit for each correction reference position. An image forming apparatus including a correction unit that performs linear interpolation processing of pixel density and corrects the density of each pixel of an image to be formed based on the result of the linear interpolation processing is described.

  In Patent Document 2, the surface of the photosensitive drum is divided into a plurality of blocks in the circumferential direction, the exposure amount is changed for each block to reduce the first periodic density unevenness, and the width of the block. Is set to a length that does not interfere with the period (pitch) of the second periodic density unevenness generated due to another factor, and an image forming apparatus that prevents generation of a streak image is described.

  Further, Patent Document 3 discloses a storage unit that stores charging potentials at two or more points on the surface of the image carrier and coordinate data expressed by the main scanning position and the sub-scanning position, and the storage unit. From the read charge potentials at the two or more points and the data of the coordinates, the charge potential of each coordinate on the surface of the image carrier or the light amount of the light source applied to reduce the unevenness of the charge potential is determined. An image forming apparatus comprising: a determination unit that determines a correction value; and a correction unit that corrects the light amount of the light source using the determined charging potential or the correction value so as to reduce the influence of charging unevenness at each coordinate. Is described.

  In Patent Document 4, at least the rotation period of the charging unit and the developing unit is set to an integral fraction of the rotation period of the image carrier, and the attribute is caused by the image carrier, the charging unit, and the developing unit. An image forming apparatus configured to include a correcting unit that corrects the density fluctuation based on the density fluctuation mode and period grasped by the density fluctuation grasping means for grasping the density fluctuation form and period is described. Yes.

JP 2009-285914 A JP 2009-53465 A JP 2009-15256 A JP 2004-109483 A

  An object of the present invention is to improve the accuracy of correcting density unevenness in an image forming apparatus.

According to the first aspect of the present invention, an image holding member, a charging unit that charges the image holding member, and the image holding member charged by the charging unit are exposed, and an electrostatic latent image is formed on the image holding member. An exposure unit that forms, a developing unit that develops the electrostatic latent image that is exposed by the exposure unit and formed on the image holding member, a transfer unit that transfers the image developed by the developing unit to a transfer target, Corresponding to an assumed location assumed on the transferred body, storage means for storing a density correction value at the corresponding location where the assumed location is actually output on the transferred body; and The image forming apparatus includes: a control unit that reads the density correction value at a corresponding location and applies the density correction value to the assumed location to control the exposure unit.
The invention according to claim 2 is a density correction value for the assumed location that includes a plurality of the assumed locations and the corresponding locations, the number of the corresponding locations is less than the number of the assumed locations, and does not have the corresponding location. The image forming apparatus according to claim 1, wherein the image forming apparatus is obtained by complementation from the position of the corresponding portion and the density correction value at the corresponding portion.
According to a third aspect of the present invention, the position of the corresponding portion is obtained from the position of the assumed portion output to the transferred body, and the density correction value is the value in the image output to the transferred body. 3. The image forming apparatus according to claim 1, wherein the image forming apparatus is obtained from the density at the position of the corresponding portion.
A fourth aspect of the present invention is the image forming apparatus according to the second or third aspect, further comprising an image reading unit that reads the position of the corresponding portion and the density at the corresponding portion.

According to the first aspect of the present invention, the density unevenness correction accuracy is improved in the image forming apparatus as compared with the case where this configuration is not provided.
According to the second aspect of the present invention, the time required for calculating the corresponding location and the density correction value can be shortened as compared with the case where the present configuration is not provided.
According to the third aspect of the present invention, the corresponding location for obtaining the density correction value to be applied to the assumed location can be obtained with higher accuracy than when the present configuration is not provided.
According to the invention of claim 4, the corresponding location and the density correction value can be automatically calculated as compared with the case where the present configuration is not provided.

It is a figure explaining an example of composition of an image forming device to which a 1st embodiment is applied. It is a figure explaining the outline | summary of the density nonuniformity correction in 1st Embodiment. 6 is a flowchart illustrating a procedure for correcting density unevenness in the first embodiment. It is a flowchart explaining the procedure of density | concentration nonuniformity correction | amendment when not using 1st Embodiment. It is a figure which shows the example of the other pattern for magnification correction. FIG. 6 is a diagram illustrating an example of a magnification correction pattern corresponding to an example of density unevenness in a sheet. It is a figure explaining an example of the composition of the image forming device to which a 2nd embodiment is applied. It is a figure explaining an example of the composition of the image forming device to which a 3rd embodiment is applied.

Embodiments of the present invention will be described below in detail with reference to the accompanying drawings.
[First Embodiment]
(Image forming apparatus 1)
FIG. 1 is a diagram illustrating an example of a configuration of an image forming apparatus 1 to which the first exemplary embodiment is applied. The image forming apparatus 1 shown here will be described by taking an intermediate transfer method generally called a tandem type as an example.
The image forming apparatus 1 illustrated in FIG. 1 includes a plurality of image forming units 10Y, 10M, 10C, and 10K that form toner images of respective color components by an electrophotographic method as a toner image forming unit. Note that when the image forming units 10Y, 10M, 10C, and 10K are not distinguished from each other, they are referred to as the image forming unit 10.
Next, as a transfer portion, a primary transfer portion 20 that sequentially transfers (primary transfer) each color component toner image formed by each of the image forming units 10Y, 10M, 10C, and 10K to the intermediate transfer belt 15, and the intermediate transfer belt 15. And a secondary transfer unit 30 as an example of a transfer unit that collectively transfers (secondary transfer) the transferred superimposed toner image onto a sheet P as an example of a transfer target. Further, a fixing unit 60 that fixes the second-transferred image on the paper P is provided as a fixing unit. In addition, the image forming control unit 50 is provided as an example of a control unit that controls the operation of each device (each unit). The image formation control unit 50 includes a density correction value storage memory 80 as an example of a storage unit that stores data (density correction value) for correcting density unevenness in order to suppress density unevenness in the formed image. Yes. Density unevenness correction (density unevenness correction) will be described later.

As shown in FIG. 1, each of the image forming units 10 </ b> Y, 10 </ b> M, 10 </ b> C, and 10 </ b> K includes a photosensitive drum 11 as an example of an image carrier that rotates in the arrow A direction, and an example of a charging unit that charges the photosensitive drum 11. And a laser exposure unit 13 as an example of exposure means for writing an electrostatic latent image on the photosensitive drum 11 (in FIG. 1, the exposure beam is indicated by Bm), and each color component toner is accommodated. And a developing unit 14 as an example of a developing unit that visualizes the electrostatic latent image on the photosensitive drum 11 with toner.
Further, a primary transfer roll 16 that transfers each color component toner image formed on the photosensitive drum 11 to the intermediate transfer belt 15 by the primary transfer unit 20, a drum cleaner 17 that removes residual toner on the photosensitive drum 11, and Have These image forming units 10Y, 10M, 10C, and 10K are linearly arranged in the order of yellow (Y), magenta (M), cyan (C), and black (K) from the upstream side of the intermediate transfer belt 15. Yes.

  The developing device 14 contains a two-component developer (hereinafter referred to as a developer) containing a nonmagnetic toner (nonmagnetic toner) and a magnetic carrier (magnetic carrier). In the developing device 14, the developer is agitated, the toner and the carrier are mixed, and a charge is imparted to the toner by rubbing and rubbing. In the developing unit 14, the consumed toner is replenished and the toner is replaced in the process of being stirred.

  The intermediate transfer belt 15 circulates (rotates) in the direction of arrow B shown in FIG. As various rolls, a drive roll 31 that circulates and drives the intermediate transfer belt 15, a support roll 32 that supports the intermediate transfer belt 15, a tension roll 33 that applies tension to the intermediate transfer belt 15 to prevent meandering, and a secondary transfer unit. 30 and a cleaning backup roll 34 provided in a cleaning section that scrapes off residual toner on the intermediate transfer belt 15.

  The primary transfer unit 20 includes a primary transfer roll 16 that faces the photosensitive drum 11 with the intermediate transfer belt 15 interposed therebetween. A voltage (primary transfer bias) having a polarity opposite to the charging polarity (minus polarity) of the toner is applied to the primary transfer roll 16, and the toner images on the photosensitive drums 11 are sequentially electrostatically attracted to the intermediate transfer belt 15, A superimposed toner image is formed on the transfer belt 15.

  The secondary transfer unit 30 includes a secondary transfer roll 22 disposed on the toner image holding surface side of the intermediate transfer belt 15 and a backup roll 25 disposed on the back surface side of the intermediate transfer belt 15 as a counter electrode of the secondary transfer roll 22. And a metal power supply roll 26 that is disposed in contact with the backup roll 25 and applies a secondary transfer bias.

  An intermediate transfer belt cleaner 35 for removing residual toner and paper dust on the intermediate transfer belt 15 after the secondary transfer is provided on the downstream side of the secondary transfer portion 30 of the intermediate transfer belt 15 so as to be contactable and separable. A reference sensor (home position sensor) 42 that generates a reference signal for taking an image forming timing in each of the image forming units 10Y, 10M, 10C, and 10K is disposed upstream of the yellow image forming unit 10Y. The reference sensor 42 recognizes a mark provided on the back side of the intermediate transfer belt 15 and generates a reference signal. Each of the image forming units 10Y, 10M, 10C, and 10K starts image formation according to an instruction from the image formation control unit 50 based on the recognition of the reference signal.

  As a recording paper transport system, a paper storage unit 70 that stores the paper P, a pickup roll 51 that takes out and transports the paper P in the paper storage unit 70, a transport roll 52 that transports the paper P, and a secondary paper P A conveyance path 53 that feeds to the transfer unit 30, a conveyance belt 55 that conveys the sheet P secondarily transferred by the secondary transfer roll 22 to the fixing unit 60, and a fixing inlet guide 56 that guides the sheet P to the fixing unit 60. Have.

  The fixing unit 60 includes a heating roll 61 containing a heating source such as a halogen lamp, and a pressure roll 62 pressed against the heating roll 61. By passing the sheet P on which the toner image is transferred between the gaps (nip portion), the toner is fixed (fixed) to the sheet P by heat and pressure. The pressure roll 62 may not be heated.

  On the other hand, the image processing apparatus 40 is connected to, for example, a personal computer (PC) 2 or an image reading apparatus (scanner) 3, and performs predetermined processing on data received from these to perform image processing on the image forming apparatus 1. It transmits to the formation control part 50. Here, a plurality of PCs 2 and image reading apparatuses 3 may be connected to the image processing apparatus 40. That is, the image processing apparatus 40 operates as a print server, receives image data from a plurality of PCs 2 and image reading apparatuses 3, and transmits the image data to the image forming apparatus 1. A plurality of image forming apparatuses 1 may be transmitted.

Next, a basic image forming process by the image forming apparatus 1 will be described.
Image data output from the PC 2 or the image reading device 3 is input to the image processing device 40. The image processing device 40 performs predetermined image processing such as shading correction, position shift correction, lightness / color space conversion, gamma correction, frame deletion, color editing, moving editing, and other various image editing. Then, the image processing device 40 transmits the image data subjected to the image processing to the image formation control unit 50 of the image forming device 1.

  The image formation control unit 50 controls the laser exposure unit 13, the charger 12, the developing unit 14, the primary transfer unit 20, the secondary transfer unit 30, and the fixing unit 60 based on the received image data subjected to image processing. To do. Hereinafter, operations of the laser exposure device 13, the charger 12, the developing device 14, the primary transfer unit 20, the secondary transfer unit 30, and the fixing unit 60 controlled by the image forming control unit 50 will be described.

  The laser exposure device 13 irradiates, for example, an exposure beam Bm emitted from a semiconductor laser to the respective photosensitive drums 11 of the image forming units 10Y, 10M, 10C, and 10K according to the input color material gradation data. After the surfaces of the photosensitive drums 11 of the image forming units 10Y, 10M, 10C, and 10K are charged by the charger 12, the surfaces are scanned and exposed by the laser exposure unit 13 to form an electrostatic latent image. The formed electrostatic latent image is developed as a toner image of each color of Y, M, C, and K by the developing device 14 in each of the image forming units 10Y, 10M, 10C, and 10K.

  Next, the toner image formed on the photoconductive drum 11 is applied to the base material of the intermediate transfer belt 15 by the primary transfer roll 16 in the primary transfer unit 20 where the photoconductive drums 11 and the intermediate transfer belt 15 are in contact with each other. Then, a voltage (primary transfer bias) having a polarity opposite to the charging polarity (minus polarity) of the toner is applied, and the toner image is sequentially superimposed on the surface of the intermediate transfer belt 15 to perform primary transfer.

  After the toner images are sequentially primary transferred onto the surface of the intermediate transfer belt 15, the intermediate transfer belt 15 moves in the direction of arrow B and conveys the toner image to the secondary transfer unit 30. The recording paper conveyance system rotates the pickup roll 51 in accordance with the timing of conveying the toner image to the secondary transfer unit 30 and supplies the paper P from the paper storage unit 70. The paper P supplied by the pickup roll 51 is conveyed by the conveyance roll 52 and reaches the secondary transfer unit 30 via the conveyance path 53. Before reaching the secondary transfer unit 30, the paper P is temporarily stopped and a registration roll (not shown) is rotated in accordance with the movement timing of the intermediate transfer belt 15 holding the toner image. Alignment with the position of the toner image is performed.

  In the secondary transfer unit 30, the secondary transfer roll 22 is pressed against the backup roll 25 via the intermediate transfer belt 15, and the unfixed toner image held on the intermediate transfer belt 15 is transferred to the intermediate transfer belt 15 and the secondary transfer belt 15. The electrostatic transfer is collectively performed on the paper P sandwiched between the rolls 22.

Thereafter, the sheet P on which the toner image has been electrostatically transferred is peeled off from the intermediate transfer belt 15 by the secondary transfer roll 22 and conveyed as it is, to the conveyance belt 55 provided on the downstream side of the secondary transfer roll 22 in the recording sheet conveyance direction. Transport. The conveyance belt 55 conveys the paper P to the fixing unit 60. The fixing unit 60 processes the unfixed toner image on the paper P with heat and pressure and fixes it on the paper P. The paper P on which the fixed image is formed is conveyed to the discharge unit of the image forming apparatus 1.
After the transfer to the sheet P is completed, the residual toner remaining on the intermediate transfer belt 15 is conveyed to the cleaning unit as the intermediate transfer belt 15 is circulated, and is intermediated by the cleaning backup roll 34 and the intermediate transfer belt cleaner 35. Remove from the transfer belt 15.

The image reading device 3 is provided on a light receiving element such as a CCD, a platen glass (not shown) on which the paper P on which an image is formed is placed, and a back side of the platen glass. A light source that emits illumination light.
Then, when the paper P on which the image is formed is placed on the front side of the platen glass, the reflected light from the paper P by the illumination light irradiated from the back side of the platen glass is guided to the CCD, whereby the paper P Read the image formed on. At this time, the illumination light from the linearly configured light source may move on the back side of the platen glass and scan the entire surface of the paper P. The illumination light from the linearly configured light source On the other hand, the paper P may be moved.

(Density unevenness correction)
“Density unevenness” refers to two-dimensional density unevenness seen on a transfer medium such as paper P on which an image is formed by the image forming apparatus 1.
In the image forming apparatus 1 shown in FIG. 1, the photosensitive drum 11, the charger 12, the developing device 14, the primary transfer roll 16, the secondary transfer roll 22, the backup roll 25, the drive roll 31, the support roll 32, and the tension roll 33. A plurality of rotating bodies such as a cleaning backup roll 34 are provided. In these rotating bodies, two-dimensional density unevenness and distortion may occur in the image formed on the paper P due to eccentricity of the rotating shaft, waviness of the surface of the rotating body, and the like.
In order to degrade the quality of the formed image, it is required to correct the density unevenness.

Further, the paper P expands or contracts (expands / contracts) due to the temperature and humidity (temperature / humidity) of the place (environment) where the image forming apparatus 1 is installed, and heating in the fixing unit 60.
Therefore, it is preferable to correct the density unevenness in consideration of the image distortion due to the eccentricity of the rotating shaft and the expansion and contraction of the paper P.

  In the correction of density unevenness, on the two-dimensional surface of the paper P, a light area (area) is darker than a predetermined density, and a dark area is lightened. That is, it is measured whether the density is lighter or darker than a predetermined density at a plurality of locations (positions) on the two-dimensional surface of the paper P. Then, a density correction value indicating a difference from a predetermined density is set for each position. Based on the density correction value, the intensity (light quantity) of the exposure beam Bm emitted from the semiconductor laser in the laser exposure unit 13 is controlled.

  The density correction value may indicate the intensity of the exposure beam Bm emitted from the semiconductor laser, or may be given as a ratio based on a predetermined intensity of the exposure beam Bm. Good. In the following description, it is assumed that the intensity of the exposure beam Bm determined in advance is given as a ratio.

In the first embodiment, the density unevenness correction is performed by assuming the position (coordinates) of the assumed location on the transfer target and the position (coordinates) of the corresponding location actually output on the paper P corresponding to the assumed location. ) And a density correction value calculation for calculating a density correction value for the corresponding portion. The density correction value is set corresponding to the assumed location.
An outline of density unevenness correction in the first embodiment will be described.

<Overview of density unevenness correction>
FIG. 2 is a diagram for explaining the outline of density unevenness correction in the first embodiment. FIG. 2A is a diagram illustrating an assumed location that the image formation control unit 50 assumes on the transfer target. As shown in FIG. 2A, it is assumed that the right direction in the drawing is the x direction (main scanning direction) and the lower direction is the y direction (sub scanning direction). An assumed location assumed on the transfer medium is indicated by “◯”.
The coordinates of the assumed locations and the density correction values corresponding to these assumed locations are stored in the density correction value storage memory 80.

The position (coordinates) of the assumed location is set by a clock signal that controls the image forming apparatus 1. That is, the position (coordinates) of the assumed location is an ideal position (coordinates) assumed in calculation. Here, it is assumed that there are a plurality of assumed locations, and both the x direction and the y direction are arranged at equal intervals. Here, the arrangement in the x direction of the position of the assumed location is denoted as A, B, C,..., And the arrangement in the y direction is denoted as 1, 2, 3,. For example, in FIG. 2A, there are six assumed locations (A, B,..., F) in the x direction and nine (1, 2,..., 9) in the y direction.
In FIG. 2 (a), the assumed locations are shown connected in a grid pattern with lines to help understanding. The assumed location is located at a grid point where the lines intersect. A figure (image) made up of assumed locations and lines connected in a grid pattern shown in FIG. 2A is denoted as assumed location image α.
Note that the assumed locations may not be arranged at equal intervals in the x direction and / or the y direction.

FIG. 2B is a diagram illustrating an assumed location image β obtained by thinning out the assumed location in order to calculate the density correction value. The assumed location image β is configured by excluding 2 rows, 4 rows, 6 rows, 8 rows, B columns, and E columns from the assumed location image α.
The density correction value may be obtained (acquired) corresponding to all the assumed locations of the assumed location image α shown in FIG. However, as the number of assumed locations increases, the time required for processing (processing time) becomes longer. Therefore, the number of assumed locations is reduced in order to shorten the processing time.

  The assumed location image β (coordinates of the assumed location of the assumed location image β) may be stored in a memory included in the image formation control unit 50, separately from the density correction value storage memory 80. Further, a user or an engineer who performs maintenance may set as necessary. Further, the image formation control unit 50 may automatically set the expected location of the assumed location image α by removing it at a predetermined rate.

  FIG. 2C is a diagram showing a magnification correction pattern for confirming the deviation (magnification) of the position (coordinates) of the assumed location of the assumed location image β on the paper P1. The magnification correction pattern is a lattice pattern in which the assumed locations of the assumed location image β shown in FIG. 2B are connected in a grid pattern in the x and y directions. The intersection of the lines corresponds to the assumed location. Here, 1, 3, 5, 7, 9 indicating rows of coordinates of assumed locations, and A, C, D, and F indicating columns are described.

FIG. 2D is a diagram showing a magnification correction pattern formed on the paper P1. As shown in FIG. 2D, the magnification correction pattern is distorted on the paper P1.
As described above, the distortion of the image is caused by the eccentricity of the rotating shaft of the rotating body and the expansion / contraction of the paper P.
The intersection of the lines constituting the magnification correction pattern on the paper P1 is a location (corresponding location) corresponding to the assumed location of the assumed location image β in the paper P1.
Then, the difference (magnification) between the position (coordinates) of the corresponding part and the coordinates of the assumed part of the assumed part image β is calculated.
The line width of the magnification correction pattern may be set to 100 to 300 dpi, for example, as long as the coordinates of the corresponding portion are obtained. The thinner the position, the more accurately the coordinates of the corresponding part can be obtained (acquired). The density correction pattern density is preferably set so that the line is easily recognized.
A method for acquiring the coordinates of the corresponding part will be described later.

  FIG. 2E is a diagram showing the corresponding location image β formed by the acquired corresponding location and the line connecting the corresponding location, and the assumed location image β in an overlapping manner. The corresponding location image β corresponds to the assumed location image β. The corresponding location image β is indicated by a solid line, and the assumed location image β is indicated by a broken line.

Each corresponding location of the corresponding location image β is deviated from each assumed location of the assumed location image β. For example, the assumed location L (A, 9) in the assumed location image β is shifted to the corresponding location R (A, 9) in the corresponding location image β. The assumed location is represented as an assumed location L (A, 9) by A, C,... Indicating the arrangement in the x direction and 1, 3,. Similarly, the corresponding location is denoted as the corresponding location R (A, 9).
The same applies to the relationship between other assumed locations and corresponding locations.
As described above, the deviation (image distortion) between the assumed location of the assumed location image β and the corresponding location of the corresponding location image β corresponding to the assumed location image β is, as described above, the eccentricity of the rotating shaft of the rotating body and the paper P. Due to the expansion and contraction of the.

  Here, as will be described later, the coordinates of the corresponding part of the corresponding part image β are acquired, and the deviation (magnification) from the corresponding part of the corresponding part image β is calculated.

FIG. 2F is a diagram illustrating an example of a correction value calculation sample.
The correction value calculation sample is an image for obtaining (calculating) a density correction value for correcting density unevenness. For example, the correction value calculation sample has the entire surface set to a density of 50%.
By setting in this way, the density on the paper P can be obtained (calculated) from the correction value calculation sample formed on the paper P (paper P2 described later).
A method for calculating the concentration will be described later.

FIG. 2G shows that the density correction value is calculated corresponding to the corresponding portion of the corresponding portion image β.
A correction value calculation sample is formed on the paper P2. Then, based on the correction value calculation sample formed on the paper P2, density correction values for correcting the density unevenness corresponding to the corresponding positions of the corresponding position image β are calculated. Here, the corresponding portion where the density correction value is calculated is indicated by “●”.

FIG. 2H is a diagram in which the corresponding location image β for which the density correction value has been calculated and the assumed location image α are superimposed. Here, the corresponding location image β is indicated by a solid line, and the assumed location image α is indicated by a broken line. The assumed location image α is shown except for an assumed location with a corresponding location. Note that the corresponding portion of the corresponding portion image β is indicated by “●” because the density correction value is calculated.
As can be seen from FIG. 2 (h), there are no corresponding locations in the assumed locations for the 2nd row, 4th row, 6th row, 8th row, Bth column, and Eth column in the assumed location image α, and the density correction value is also calculated. Not.

FIG. 2 (i) shows a corresponding location image α obtained by complementing the corresponding location of the corresponding location image β with respect to an assumed location having no corresponding location in the corresponding location image β in the assumed location image α, and obtaining the coordinates of the corresponding location. FIG. The corresponding location image α corresponds to the assumed location image α. Similarly, the density correction value is also calculated by complementing the density correction value at the corresponding part of the corresponding part image β. Therefore, all corresponding portions are indicated by “●”.
In FIG. 2 (i), the coordinates of the corresponding part not included in the corresponding part image β are obtained from the adjacent corresponding part by linear interpolation.
In addition, for the complement of the coordinates of the corresponding portion and the density correction value, other complement methods such as a weighted complement may be used instead of the linear complement. Further, the coordinates and density correction value of the corresponding part not included in the corresponding part image β are included in the corresponding part image β surrounding the corresponding part in addition to the corresponding part included in the corresponding part image β adjacent to the corresponding part. It may be obtained in consideration of the corresponding location.

  Then, the density correction value at each corresponding location in the corresponding location image β is stored in the density correction value storage memory 80 as the density correction value at the corresponding assumed location in the assumed location image α. For example, the density correction value corresponding to the assumed location L (A, 9) in FIG. 2E is the density correction value calculated at the corresponding location R (A, 9) corresponding to the assumed location L (A, 9). Become.

  In addition, it is preferable to perform density unevenness correction for each color component. If the density unevenness is corrected for each color component, the density unevenness is corrected even when they are superimposed.

As described above, each assumed location of the assumed location image α set in the image forming control unit 50 corresponds to each corresponding location image α (including the corresponding location for which coordinates are obtained by complementation) on the paper P. It shifts to the place.
Therefore, in the first embodiment, the density correction value to be set in each assumed location of the assumed location image α is set as the density correction value in the corresponding location set in the corresponding location image α.

That is, as shown in FIG. 2E, the assumed location L (A, 9) of the assumed location image β is shifted to the corresponding location R (A, 9). Here, when the density correction value obtained at the assumed location L (A, 9) in FIG. 2E is used as the density correction value for the assumed location L (A, 9), the corresponding location R (A, 9) is used. The density correction value at the assumed location L (A, 9) is applied. That is, the density unevenness correction is performed based on the density correction value obtained from the density unevenness at different positions. Therefore, the density unevenness correction includes an error.
In contrast, in the first embodiment, the assumed location L (A, 9) of the assumed location image α is shifted to the corresponding location R (A, 9). However, since the density correction value at the corresponding location R (A, 9) is calculated, the density correction value at the corresponding location R (A, 9) is applied to the corresponding location R (A, 9). That is, in the density unevenness correction, the density correction value is applied to the position (coordinate) where the density correction value is calculated. Therefore, the accuracy of density unevenness correction is improved.
In this way, in the first embodiment, even if the position (coordinates) of the assumed location on the paper P is deviated, the density unevenness correction accuracy is suppressed from degrading due to the deviation.

Here, the assumed location image β is configured by thinning a plurality of assumed locations from the assumed location image α. The assumed location image α may be the assumed location image β without thinning out the assumed location.
In the case where the number of assumed places of the assumed place image α and the assumed place image β is different, the number of assumed places included in the assumed place image α is required for the accuracy of complementation and the complementation of the assumed place image β by the assumed place. It may be set in consideration of the required time.

The accuracy of density unevenness correction increases as the number of assumed locations included in the assumed location image β increases. However, when the number of assumed locations increases, the position (coordinate) shift between the assumed location and the corresponding location and the processing time for obtaining the density correction value become longer. Therefore, the number of assumed locations included in the assumed location image β may be set in consideration of the accuracy of correction, the time required to calculate the density correction value, and the like.
Also, the smaller the density unevenness on the paper P, the less the error (error) due to complementation occurs. Therefore, the number of assumed locations in the assumed location image β may be set in consideration of the density unevenness on the paper P.

<Density unevenness correction procedure>
FIG. 3 is a flowchart for explaining a procedure for correcting density unevenness in the first embodiment. With reference to FIG. 2, the procedure for correcting density unevenness in the first embodiment will be described according to the flowchart of FIG. The density unevenness correction may be executed by a user or a maintenance engineer pressing a predetermined button or switch. The image forming apparatus 1 determines the temperature and / or humidity in advance. It may be executed when it is sensed that a change has occurred beyond a specified range. It can be suppressed that the accuracy of density unevenness correction is deteriorated due to the distortion of the image due to the expansion and contraction of the paper P due to the change in temperature and / or humidity.
The density unevenness correction may be executed when the image forming apparatus 1 forms a predetermined number of images. It is possible to suppress deterioration in density unevenness accuracy due to changes with time of various rotating bodies.
Here, since the density unevenness correction procedure is a procedure for setting the density correction value in the density correction value storage memory 80, it will be referred to as a “density correction value setting mode”.

Here, the image formation control unit 50 includes a calculation unit such as a CPU, and the calculation unit obtains (calculates) the position (coordinates) and the density correction value of the corresponding portion, and the density correction value is input to the image formation control unit. Description will be made assuming that the data is stored in the 50 density correction value storage memory 80. However, a PC or the like provided with a calculation unit may be provided separately from the image formation control unit 50.
The density correction value storage memory 80 is provided inside the image formation control unit 50, but may be provided outside the image formation control unit 50. The position (coordinates) of the corresponding location, the density correction value, and the like may be obtained by the calculation means, and the density correction value may be stored.

When the density correction value setting mode starts, the image formation control unit 50 determines whether or not to output the magnification correction pattern shown in FIG. 2C (Yes / No) (step 1). In FIG. 3 and FIG. 4, “step” is expressed as “S”.
In this determination, the magnification correction pattern has already been output to the paper P1, and the position (coordinates) of the corresponding portion of the corresponding portion image β shown in FIG. If it is not necessary to obtain the position (coordinates) of the corresponding location of the location image β, the determination is No.
On the other hand, when the user or the engineer who performs maintenance instructs the output of the magnification correction pattern, or when the change in temperature and / or humidity exceeds a predetermined range, it is determined as Yes.
In this manner, a plurality of states can be assigned to each determination of Yes / No.
Hereinafter, a case where a positive determination (Yes) is made in Step 1 will be described, and a case where a negative determination (No) is made will be described later.

  The image forming control unit 50 controls the image forming unit 10 and the like to output (form) a magnification correction pattern on the paper P1 (step 2) (see FIG. 2D).

The magnification correction pattern output on the paper P1 is read by the image reading device 3 (step 3). Here, the sheet P1 on which the magnification correction pattern is output is placed on the platen glass of the image reading device 3 by the user or the like.
Then, the image reading device 3 detects the reflected light from the paper P1 through, for example, red (R), green (G), and blue (B) filters, and correspondingly, for example, 8 bits (256 gradations). Generate output data. From this output data, the position on the paper P1 and the density corresponding to the position are obtained (calculated) and transmitted to the image formation control unit 50 as digital data. For example, if the reading resolution of the image reading device 3 is 600 dpi in the horizontal direction (x direction shown in FIG. 2) and the vertical direction (y direction shown in FIG. 2), respectively, Concentrations are obtained for 4961 positions (coordinates) in total, 4961 in the horizontal direction and 7016 in the vertical direction. The density is, for example, 8-bit (256 gradations) data at each position (coordinate).
Here, the image reading device 3 is described as calculating the density, but the image forming control unit 50 or other computing means may calculate the density.

  Thereafter, the image formation control unit 50 obtains the position (coordinates) of the intersection (corresponding part) of the line of the magnification correction pattern from the position (coordinates) and density digital data received in step 3 (step 4). The position (coordinates) of the line is obtained by scanning in the x direction or the y direction in the digital data of the position (coordinates) and density received in step 3 to obtain a position (coordinates) with high density. The intersecting position (coordinates) is obtained as the intersection of the obtained lines. This intersection is a corresponding location. By obtaining all the corresponding locations, the corresponding location image β in FIG. 2E is obtained.

  Then, the deviation (magnification) of the position (coordinates) of each corresponding location in the corresponding location image β from each corresponding expected location in the assumed location image β is calculated (step 5). The deviation (magnification) may be represented by a magnification in the x direction and a magnification in the y direction, for example, in the xy coordinates.

  Next, the correction value calculation sample is output to the paper P2 (step 6). For example, the correction value calculation sample is set to have a density of 50% over the entire surface.

Then, the paper P2 on which the correction value calculation sample is output is read by the image reading device 3 (step 7). Also here, the sheet P2 on which the correction value calculation sample is output is placed on the platen glass of the image reading device 3 by the user or the like.
The reading of the correction value calculation sample here is performed in the same manner as the reading of the magnification correction pattern on the paper P1 in step 3. That is, for example, with respect to A4 size paper P, the density is obtained with 8 bits (256 gradations) for 4961 positions (coordinates) in total, 4961 in the horizontal direction, 7016 in the vertical direction, and digital data. To the image formation control unit 50.

  At this time, the sheet P1 from which the magnification correction pattern is output and the sheet P2 from which the correction value calculation sample is output are placed on the platen glass of the image reading device 3 with a positional deviation amount within a predetermined allowable range. It is done. For example, a sheet P1 on which a magnification correction pattern is output and a sheet P2 on which a correction value calculation sample is output are placed by pressing against a positioning member such as a corner provided in the image reading device 3.

And the density | concentration in the position (coordinate) of the assumption location of the corresponding location image (beta) is calculated | required from the digital data of a position (coordinate) and density | concentration (step 8). In step 5, the magnification of the corresponding part in the corresponding part image β is calculated. Therefore, the position (coordinates) of the corresponding portion in the correction value calculation sample may be set with this magnification, and the density at that position may be acquired.
Note that the position (coordinates) of the corresponding part in the correction value calculation sample may be set by the position (coordinate) of the corresponding part obtained in step 4, and the density at that position may be acquired. In this case, the process of step 5 is not necessary.

  Thereafter, a density correction value for setting to increase or decrease the density is calculated in comparison with a predetermined density (reference density) (step 9). At this time, the magnification and the density correction value are also supplemented for the assumed location of the assumed location image α that is not included in the corresponding location image β.

  The density correction value calculated in this way is stored in the density correction value storage memory 80 as a density correction value corresponding to the assumed location image α (step 10).

On the other hand, if “No” is determined in step 1, the calculation of the magnification of the position of the corresponding portion by the magnification correction pattern has already been completed, so the correction value calculation sample in step 6 is output to the paper P 2. Just migrate.
For example, this may be performed when a plurality of correction value calculation samples having different densities are used to set a plurality of density correction values for each of the plurality of correction value calculation samples.
Further, an image formation called a multiple type in which each color component toner of yellow (Y), magenta (M), cyan (C), and black (K) is accommodated around one photosensitive drum and includes a plurality of developing devices. This may be performed when the density correction value is set corresponding to each color component in an apparatus or the like.

  As described above, in the first embodiment, the density correction value set for each assumed location of the assumed location image α corresponds to each assumed location of the assumed location image α on the paper P2. This is the density correction value at the corresponding location. Therefore, the accuracy of density unevenness correction is improved.

  FIG. 4 is a flowchart for explaining the procedure for correcting density unevenness when the first embodiment is not used. Here, the magnification correction pattern is not output in step 2 of FIG. Therefore, the process starts from step 6 in FIG. Note that, unlike the first embodiment, the magnification of the position (coordinates) of the corresponding location is not calculated. Hereinafter, a description will be given with reference to FIG.

First, a correction value calculation sample is output to the paper P2 (step 21). This is the same as step 6 in FIG. For the correction value calculation sample, for example, the entire surface is set to 50% density.
Then, the paper P2 on which the correction value calculation sample is output is read by the image reading device 3 (step 22). This is also the same as step 7 shown in FIG. For example, for A4 size paper P, the density is obtained with 8 bits (256 gradations) for 4961 positions (coordinates) in total, 4961 in the horizontal direction, 7016 in the vertical direction, and the image is converted into digital data. It is transmitted to the formation control unit 50.

And the density | concentration in the position (coordinate) of each assumption location of the assumption location image (beta) shown in FIG.2 (b) is acquired from the digital data of a position (coordinate) and density | concentration (step 23). Note that the position (coordinates) of each assumed location of the assumed location image β is determined in advance. Therefore, the density at the assumed location of the assumed location image β can be easily acquired from the digital data of the position (coordinates) and the density.
Note that the assumed location image α shown in FIG. 2A may be used instead of the assumed location image β.
In the case of using the first embodiment, the density at the corresponding location was acquired. When the first embodiment is not used, the density at the assumed location is acquired.

  Thereafter, a density correction value for setting to increase or decrease the density is calculated in comparison with a predetermined density (reference density) (step 24). At this time, the magnification and the density correction value are also supplemented for an assumed location of the assumed location image α that is not included in the assumed location image β.

  The density correction value calculated in this way is stored in the density correction value storage memory 80 as a density correction value corresponding to the assumed location image α (step 25).

When the first embodiment is not used, image distortion due to eccentricity of the rotating shaft of the rotating body and expansion / contraction of the paper P is not considered. That is, it is not known to which position on the paper P2 each assumed place of the assumed place image α corresponds (reflected). Therefore, the density correction value for correcting the density unevenness is set for a hypothetical (theoretical) assumed location set by the image formation control unit 50. That is, as described in relation to the assumed location image β and the corresponding location image β in FIG. 2E, the assumed location image β becomes the corresponding location image β on the paper P. For example, the assumed location L (A, 9) is shifted to the corresponding location R (A, 9). Therefore, it is necessary to set the density correction value for the assumed location L (A, 9) with the density of the corresponding location R (A, 9).
However, in the case where the first embodiment is not used, the concentration (assumed when the assumed location L (A, 9) is not shifted although it is shifted to the corresponding location R (A, 9). The density correction value is set according to the density of the location L (A, 9). That is, when the present embodiment is not used, the density correction value calculated based on the density at a position different from the position of the assumed location on the paper P is used as the density correction value of the assumed location, so the density unevenness correction accuracy is Will be lower.

  On the other hand, in the first embodiment, since the density correction value calculated based on the density at the position of the corresponding location on the paper P is used as the density correction value of the corresponding location, the first embodiment is used. Compared to the case where there is no density unevenness correction accuracy is high.

The interval between the assumed locations of the assumed location image α is, for example, 5 mm. If it is set smaller than 5 mm, the accuracy of density unevenness correction is improved. However, the capacity (memory size) of the density correction value storage memory 80 increases. Therefore, the interval between the assumed locations of the assumed location image α may be determined by the required density unevenness correction accuracy, the capacity (memory size) of the density correction value storage memory 80, and the like.
It should be noted that the interval between the dots written by the laser exposure unit 13 on the photosensitive drum 11 is smaller than the interval between the assumed locations of the assumed location image α. Therefore, the amount of light for each dot is further complemented and set based on the density correction value at the assumed location.

<Magnification correction pattern>
Next, the magnification correction pattern will be further described.
In the magnification correction pattern in FIG. 2C, the lines are provided in a grid pattern. As a result, the position (coordinates) of the assumed location was obtained two-dimensionally with the intersection of the lines as the assumed location.
FIG. 5 is a diagram illustrating another example of the magnification correction pattern. FIG. 5A shows a case where a line is provided in the y direction (sub-scanning direction) and no line is provided in the x direction (main scanning direction). FIG. 5B shows a case where lines are provided in the x direction (main scanning direction) and no lines are provided in the y direction (sub-scanning direction), contrary to FIG.

As shown in FIG. 5A, when a line is provided in the y direction (sub-scanning direction), a positional shift (magnification) is obtained in the x direction (main scanning direction). This is a case where there is no positional shift in the y direction (sub-scanning direction) (magnification is 1). The position in the y direction where the density correction value is set may be a position set by the image formation control unit 50.
As shown in FIG. 5B, when a line is provided in the x direction (main scanning direction), a positional shift (magnification) is obtained in the y direction (sub scanning direction). This is a case where there is no position shift (magnification is 1) in the x direction (main scanning direction). The position in the x direction where the density correction value is set may be a position set by the image formation control unit 50.
As described above, the magnification correction pattern may be in a lattice shape in which a plurality of lines intersect as shown in FIG. 2C, and the plurality of lines are arranged as shown in FIGS. 5A and 5B. It is not necessary to cross.
Although not shown, a plurality of dots are not crossed, but a dot having a predetermined size that does not interfere with reading is used as a magnification correction pattern at the intersection when the plurality of lines cross each other. You may provide as.

Further, in FIG. 2C, the magnification correction pattern is configured by providing two lines at the center and one line at both ends in the x direction and five lines at equal intervals in the y direction. It was. In FIG. 5A, the magnification correction pattern is composed of six lines provided at equal intervals in the x direction. In FIG. 5B, the magnification correction pattern is composed of nine lines provided at equal intervals in the y direction.
These magnification correction patterns are provided with lines so as to be symmetrical with respect to the center of the paper P in the left and right or / and up and down directions.

FIG. 6 is a diagram illustrating an example of a magnification correction pattern corresponding to an example of density unevenness in the paper P. In each of FIGS. 6A to 6C, an example of density unevenness is shown on the left side of the figure, and an example of a magnification correction pattern is shown on the right side of the figure. In the magnification correction pattern, the solid line portion is a portion provided with a line, and the broken line portion is not provided with a line.
6A shows an area (area) 81 biased to the right on the upper side of the paper P, an area 82 biased to the left at the upper and lower centers of the paper P, and an area 83 biased to the right on the lower side. This shows a case where the density unevenness is larger than that of the area. FIG. 6B shows a case where the density unevenness is larger in the left area 84 and the right area 85 of the paper P than in other areas. FIG. 6C illustrates a case where the density unevenness is larger in the upper area 86 and the lower area 87 of the paper P than in other areas. In these cases, as shown on the right side of the figure, the magnification correction pattern is set in the areas 81 to 87 where the density unevenness is large, and the density correction values are set for the areas 81 to 87 where the density unevenness is large. The density correction value may not be set for an area where the density unevenness is small.
Since the image forming apparatus 1 uses a plurality of rotating bodies as described above, density unevenness may occur in a specific area of the paper P shown in FIG. 6 due to the eccentricity of the rotating shaft of the rotating body. If an area with large density unevenness is known in advance, as shown in FIG. 6, a density correction value is calculated for an area with large density unevenness, and a density correction value is not calculated for an area with small density unevenness (the density correction value is set to 0). It is also possible to do this. Thus, by limiting the area for setting the density correction value, the time required for calculating the density correction value can be shortened.

[Second Embodiment]
FIG. 7 is a diagram illustrating an example of the configuration of the image forming apparatus 1 to which the second exemplary embodiment is applied. The image forming apparatus 1 according to the second embodiment further includes an image reading unit 90 that reads an image formed on the paper P on the exit side of the fixing unit 60 in the image forming apparatus 1 according to the first embodiment. I have.
The image reading unit 90 is connected to the image formation control unit 50 and transmits data related to the read image to the image formation control unit 50.

The image reading unit 90 is provided in a direction orthogonal to the conveyance direction (arrow C direction) of the paper P, and includes a linear light source 91 that irradiates the surface of the paper P, a linear CCD, and the like. A light receiving element 92 that receives the reflected light, a plurality of reflecting mirrors 93 that reflect the reflected light from the paper P and guide it to the light receiving element 92, and a lens 94 that reduces and irradiates the guided light to the light receiving element 92. And.
Since the paper P moves in the direction of arrow C, the image reading unit 90 reads an image formed on the paper P as the paper P moves.

In the second embodiment, instead of the image reading device 3 in the first embodiment, the image reading unit 90 calculates the magnification correction pattern output to the paper P1 and the density correction value output to the paper P2. Read the sample.
As described above, in the first embodiment, the sheet P1 on which the magnification correction pattern is output and the sheet P2 on which the correction value calculation sample is output are placed on the platen glass of the image reading device 3 by the user or the like. It was on.
On the other hand, in the second embodiment, the magnification correction pattern output to the paper P1 and the correction value calculation sample output to the paper P2 can be automatically read following the processing of the fixing unit 60.
Since the outline and procedure of density unevenness correction are the same as those in the first embodiment, description thereof will be omitted.

7 requires a reflecting mirror 93, a lens 94, and the like in order to reduce the reflected light from the paper P and irradiate the light receiving element 92 with it. For this reason, the image reading unit 90 becomes large.
On the other hand, as the image reading unit 90, a proximity type or close contact type light receiving element that is disposed in the vicinity of the paper P and receives reflected light from the paper P may be used. Since the light receiving element is a proximity type or a contact type, the image reading unit 90 can be made small.

[Third Embodiment]
FIG. 8 is a diagram illustrating an example of the configuration of the image forming apparatus 1 to which the third exemplary embodiment is applied. The image forming apparatus 1 according to the third embodiment is the downstream side of the primary transfer unit 20 of all the image forming units 10 and the secondary transfer unit 30 in the image forming apparatus 1 according to the first embodiment. An image reading unit 95 is further provided on the upstream side.
The image reading unit 95 has the same configuration as the image reading unit 90 of the image forming apparatus 1 according to the second embodiment. That is, the intermediate transfer belt 15 is provided in a direction orthogonal to the moving direction (arrow B direction) of the intermediate transfer belt 15 and is configured by a linear light source 96 that irradiates the surface of the intermediate transfer belt 15 and a linear CCD. A light receiving element 97 that receives the reflected light from the intermediate transfer belt 15, a plurality of reflecting mirrors 98 that reflect the reflected light from the intermediate transfer belt 15 and guide it to the light receiving element 97, and reduce the guided light to the light receiving element 97. And a lens 99 for irradiating.
The intermediate transfer belt 15 moves in the arrow B direction. Therefore, the image reading unit 95 reads an image formed on the intermediate transfer belt 15 as the intermediate transfer belt 15 moves.
In the third embodiment, the intermediate transfer belt 15 is an example of a transfer target, and the primary transfer unit 20 is an example of a transfer unit.

In the third embodiment, a density correction value for correcting density unevenness is set with respect to a position (coordinates) on the intermediate transfer belt 15 at the set assumed location. On the other hand, in the first embodiment and the second embodiment, the density correction value for correcting the density unevenness with respect to the position (coordinates) of the corresponding location on the paper P corresponding to the set assumed location is set. Set. That is, in the first embodiment and the second embodiment, a density correction value for correcting density unevenness is set in consideration of a shift in position (coordinates) between an assumed location and a corresponding location on the paper P. ing. On the other hand, in the third embodiment, a density correction value for correcting density unevenness is set in consideration of a shift in position (coordinates) between an assumed location and a corresponding location on the intermediate transfer belt 15.
In the third embodiment, density unevenness seen on the intermediate transfer belt 15 can be corrected. However, the density unevenness caused by the fixing process of the fixing unit 60 cannot be corrected. For this reason, the present invention can be applied when the density unevenness generated in the processing of the fixing unit 60 is not corrected or when the density unevenness is not a problem.
Unlike the first embodiment and the second embodiment, the third embodiment does not use the paper P1 that outputs the magnification correction pattern and the paper P2 that outputs the correction value calculation sample. It is possible to suppress a decrease in the density unevenness correction accuracy due to the positional deviation between the sheets P.

  Since the outline and procedure of density unevenness correction are the same as those in the first embodiment, description thereof will be omitted. Note that the sheet P in the first embodiment may be replaced with the intermediate transfer belt 15.

DESCRIPTION OF SYMBOLS 1 ... Image forming apparatus, 2 ... PC, 3 ... Image reading device 10, 10Y, 10M, 10C, 10K ... Image forming unit, 11 ... Photosensitive drum, 12 ... Charger, 13 ... Laser exposure device, 14 ... Development 15 ... intermediate transfer belt, 20 ... primary transfer unit, 30 ... secondary transfer unit, 40 ... image processing apparatus, 50 ... image formation control unit, 60 ... fixing unit, 80 ... density correction value storage memory, 90, 95 ... Image reading unit

Claims (4)

An image carrier,
Charging means for charging the image carrier;
Exposing the image carrier charged by the charging unit to form an electrostatic latent image on the image carrier;
Developing means for developing the electrostatic latent image exposed by the exposure means and formed on the image carrier;
Transfer means for transferring the image developed by the developing means to a transfer target;
Storage means for storing density correction values at corresponding locations where the assumed location is actually output on the transferred body in correspondence with the assumed location assumed on the transferred body;
An image forming apparatus comprising: a control unit that reads out the density correction value at the corresponding location from the storage unit and applies the density correction value to the assumed location to control the exposure unit.   The assumed location and the corresponding location are plural, the number of the corresponding locations is less than the number of the assumed locations, and the density correction value for the assumed location that does not have the corresponding location is the position of the corresponding location and the relevant location. The image forming apparatus according to claim 1, wherein the image forming apparatus is obtained by complementation from the density correction value at a corresponding location.   The position of the corresponding location is obtained from the position of the assumed location output to the transferred body, and the density correction value is obtained from the density at the position of the corresponding location in the image output to the transferred body. The image forming apparatus according to claim 1, wherein the image forming apparatus is an image forming apparatus.   The image forming apparatus according to claim 2, further comprising an image reading unit that reads the position of the corresponding portion and the density at the corresponding portion.

Images