Image forming apparatus
Patent Information
- Application Number
- JP2022048422
- Authority / Receiving Office
- JP · JP
- Patent Type
- Applications
- Current Assignee / Owner
- Filing Date
- 2022-03-24
- Publication Date
- 2025-03-18
- Estimated Expiration
- 2042-03-24
AI Technical Summary
Existing image forming apparatuses experience density unevenness due to variations in light amount not only between chips but also within each chip, leading to inconsistencies in the formed images.
The apparatus employs a configuration with staggered arrangements of light emitting chips and elements, controlled by a current control mechanism that adjusts current flow based on image data and correction means to correct light amount variations, using a two-stage correction process to ensure uniform exposure across the photoreceptor.
This approach effectively suppresses density unevenness in images by precisely controlling light emission, ensuring high-quality image formation without increasing circuit complexity.
Smart Images

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Abstract
Description
Technical Field
[0001] The present invention relates to an electrophotographic image forming apparatus.
Background Art
[0002] An electrophotographic image forming apparatus forms an electrostatic latent image on a photoreceptor by exposing the photoreceptor that is rotationally driven, and forms an image by developing the electrostatic latent image with toner. Note that the direction parallel to the rotation axis of the photoreceptor is referred to as the main scanning direction. Patent Document 1 discloses an image forming apparatus in which a plurality of chips each having a plurality of light emitting elements are arranged in the main scanning direction and exposure for one line in the main scanning direction is performed. Patent Document 1 discloses a configuration for correcting density unevenness due to a difference in light amount between two adjacent chips in the main scanning direction.
Prior Art Documents
Patent Documents
[0003]
Patent Document 1
Summary of the Invention
Problems to be Solved by the Invention
[0004] However, the difference in light amount can occur not only between chips but also between a plurality of light emitting elements within a chip. Therefore, even if only the difference in light amount between chips is corrected, density unevenness may occur in the formed image. That is, density unevenness occurs in the image formed by the configuration in Patent Document 1.
[0005] In view of the above problems, an object of the present invention is to suppress density unevenness in a formed image.
Means for Solving the Problems
[0006] According to one aspect of the present invention, an image forming apparatus for forming an image on a sheet includes a photoreceptor and a plurality of light-emitting chips arranged at different positions in the main scanning direction, each of the plurality of light-emitting chips having a plurality of light-emitting elements arranged at different positions in the main scanning direction and a current control means for controlling the current flowing through the plurality of light-emitting elements based on a set value. The apparatus comprises an exposure head that forms an electrostatic latent image on the photoreceptor by repeatedly exposing one line in the main scanning direction of the rotationally driven photoreceptor to the plurality of light-emitting chips, each of the plurality of light-emitting chips having a plurality of light-emitting elements, and a developing means for developing the electrostatic latent image on the photoreceptor to form an image on the photoreceptor and a correction means for suppressing light intensity unevenness of the exposure head, wherein the correction means suppresses light intensity unevenness of the exposure head by correcting the image data and setting a set value for each of the plurality of light-emitting chips. [Effects of the Invention]
[0007] According to the present invention, density unevenness in the formed image can be suppressed. [Brief explanation of the drawing]
[0008] [Figure 1] A diagram illustrating the configuration of an image forming apparatus according to one embodiment. [Figure 2] A diagram showing an exposure head and photoreceptor according to one embodiment. [Figure 3] A diagram showing a printed circuit board of an exposure head according to one embodiment. [Figure 4] A diagram illustrating the arrangement of light-emitting elements within a light-emitting chip according to one embodiment. [Figure 5] A plan view of a light-emitting chip according to one embodiment. [Figure 6] A cross-sectional view of a light-emitting chip according to one embodiment. [Figure 7] A diagram showing a spot in a photoreceptor according to one embodiment. [Figure 8] A control configuration diagram for each light-emitting chip according to one embodiment. [Figure 9]A block diagram of the inside of a light-emitting chip according to one embodiment. [Figure 10] A block diagram of a light intensity correction unit according to one embodiment. [Figure 11] An explanatory diagram of the processing in the light intensity correction unit according to one embodiment. [Figure 12] A diagram showing a light intensity correction chart according to one embodiment. [Figure 13] A diagram illustrating the process of generating correction information according to one embodiment. [Figure 14] A diagram illustrating the process of generating correction information according to one embodiment. [Figure 15] A diagram illustrating the process of generating correction information according to one embodiment. [Modes for carrying out the invention]
[0009] The embodiments will be described in detail below with reference to the attached drawings. Note that the following embodiments do not limit the invention as defined in the claims. While the embodiments describe multiple features, not all of these features are essential to the invention, and the features may be combined in any way. Furthermore, in the attached drawings, identical or similar configurations are given the same reference numerals, and redundant descriptions are omitted.
[0010] Figure 1 is a schematic diagram of the image forming apparatus according to this embodiment. The reading unit 100 optically reads a document placed on the document glass and generates image data representing the reading result. The image forming unit 103 forms an image on a sheet, for example, based on the image data generated by the reading unit 100, or based on image data received from an external device via a network.
[0011] The image forming unit 103 includes image forming units 101a, 101b, 101c, and 101d. The image forming units 101a, 101b, 101c, and 101d form toner images of black, yellow, magenta, and cyan respectively. The configurations of the image forming units 101a, 101b, 101c, and 101d are the same, and hereinafter they will also be collectively referred to as the image forming unit 101. The photoreceptor 102 of the image forming unit 101 is rotationally driven in the clockwise direction in the figure during image formation. The charger 107 charges the photoreceptor 102. The exposure head 106 exposes the photoreceptor 102 according to image data to form an electrostatic latent image on the photoreceptor 102. The developing device 108 develops the electrostatic latent image on the photoreceptor 102 with toner. The toner image on the photoreceptor 102 is transferred to a sheet being conveyed on the transfer belt 111. By overlapping and transferring the toner images of each photoreceptor 102, colors different from black, yellow, magenta, and cyan can be reproduced.
[0012] The conveying unit 105 controls the feeding and conveyance of sheets. Specifically, the conveying unit 105 feeds a sheet from a designated unit among the internal storage units 109a and 109b, the external storage unit 109c, and the manual unit 109d to the conveyance path of the image forming apparatus. The fed sheet is conveyed to the registration roller 110. The registration roller 110 conveys the sheet onto the transfer belt 111 at a predetermined timing so that the toner image of each photoreceptor 102 is transferred to the sheet. As described above, while being conveyed on the transfer belt 111, a toner image is transferred to the sheet. The fixing unit 104 fixes the toner image to the sheet by heating and pressing the sheet onto which the toner image has been transferred. After the fixing of the toner image, the sheet is discharged to the outside of the image forming apparatus by the discharge roller 112. An optical sensor 113 is disposed at the opposing position of the transfer belt 111. The optical sensor 113 detects a test chart for measuring the amount of color deviation formed on the transfer belt 111 by the image forming unit 101. Based on the detection result of the test chart, a control unit (not shown) performs color deviation correction control.
[0013] Figures 2(A) and 2(B) show the photoreceptor 102 and the exposure head 106. The exposure head 106 includes a group of light-emitting elements 201, a printed circuit board 202 on which the group of light-emitting elements 201 is mounted, a rod lens array 203, and a housing 204 for attaching the rod lens array 203 to the printed circuit board 202. The rod lens array 203 focuses the light emitted by the group of light-emitting elements 201 onto the photoreceptor 102 to form an image spot of a predetermined size (hereinafter simply referred to as the spot) on the photoreceptor 102.
[0014] Figures 3(A) and 3(B) show the printed circuit board 202. Figure 3(A) shows the side on which the connector 305 is mounted, and Figure 3(B) shows the side on which the light-emitting element group 201 is mounted (the side opposite to the side on which the connector 305 is mounted). In this embodiment, the light-emitting element group 201 has 20 light-emitting chips 400-1 to 400-20. The light-emitting chips 400-1 to 400-20 are arranged in a staggered pattern in two rows along the main scanning direction. More specifically, the light-emitting chips 400-(2k-1) (where k is an integer from 1 to 10) are arranged in a single row along the main scanning direction, and the light-emitting chips 400-2k are arranged in a single row along the main scanning direction. The position of the row of light-emitting chips 400-(2k-1) in the sub-scanning direction is different from the position of the row of light-emitting chips 400-2k in the sub-scanning direction. The sub-scanning direction corresponds to the direction in which the photoreceptor 102 rotates. Furthermore, the sub-scanning direction is perpendicular to the main scanning direction. In the following description, light-emitting chips 400-1 to 400-20 will be collectively referred to as light-emitting chip 400. Also, light-emitting chip 400-(2k-1) will be referred to as an odd-numbered light-emitting chip 400, and light-emitting chip 400-2k will be referred to as an even-numbered light-emitting chip 400. Each light-emitting chip 400 has multiple light-emitting elements. Each light-emitting chip 400 on the printed circuit board 202 is connected to the image controller 800 (Figure 8), which is the control unit, via a connector 305.
[0015] FIG. 4 is an explanatory diagram of the arrangement of the light-emitting chip 400. In the light-emitting chip 400, 748 light-emitting elements 602 arranged along the main scanning direction are arranged in 4 sets in the sub-scanning direction. The pitch of adjacent light-emitting elements 602 in the main scanning direction is approximately 21.16 μm corresponding to a resolution of 1200 dpi. Therefore, the length of one set of 748 light-emitting elements in the main scanning direction is approximately 15.8 mm. Each set is arranged by shifting approximately 5 μm in the main scanning direction corresponding to a resolution of 4800 dpi. Also, the light-emitting chips 400 in the even-numbered columns and the light-emitting chips 400 in the odd-numbered columns are arranged so as to overlap in the main scanning direction. The interval Ly between the light-emitting elements 602 of the light-emitting chips 400 in the even-numbered columns and the light-emitting elements 602 of the light-emitting chips 400 in the odd-numbered columns is, for example, approximately 105 μm.
[0016] FIG. 5 is a plan view of the light-emitting chip 400. The light-emitting chip 400 includes a light-emitting portion 404 including a plurality of light-emitting elements 602. The light-emitting portion 404 is formed on the light-emitting substrate 402. Further, a circuit portion 406 for controlling the light-emitting portion 404 is provided on the light-emitting substrate 402. A line for communicating with the image controller 800 is connected to the pad 408.
[0017] FIG. 6 shows a part of the cross section taken along the line A-A in FIG. 5. A plurality of lower electrodes 504 are formed on the light-emitting substrate 402. A gap of length dx is provided between two adjacent lower electrodes 504. A light-emitting layer 506 is provided on the lower electrode 504, and an upper electrode 508 is provided on the light-emitting layer 506. The upper electrode 508 is a common electrode for the plurality of lower electrodes 504. When a predetermined voltage is applied between the lower electrode 504 and the upper electrode 508, a current flows from the lower electrode 504 to the upper electrode 508, and the light-emitting layer 506 emits light. That is, the lower electrode 504 is provided corresponding to one light-emitting element 602. By increasing the length dx with respect to the length dz between the lower electrode 504 and the upper electrode 508, the leakage current between adjacent lower electrodes 504 can be suppressed, and the mis-emission of adjacent light-emitting elements 602 can be suppressed.
[0018] For example, an organic EL film can be used for the light-emitting layer 506. Alternatively, an inorganic EL film can be used for the light-emitting layer 506. The upper electrode 508 is composed of a transparent electrode, such as indium tin oxide (ITO), so as to transmit the emission wavelength of the light-emitting layer 506. In this embodiment, the entire upper electrode 508 transmits the emission wavelength of the light-emitting layer 506, but it is not necessary for the entire upper electrode 508 to transmit the emission wavelength. Specifically, it is sufficient for the region from which light is emitted from each light-emitting element 602 (corresponding to the lower electrode 504) to transmit the emission wavelength.
[0019] As explained using Figure 4, one light-emitting chip 400 has four sets of multiple light-emitting elements 602 arranged along the main scanning direction, and in the sub-scanning direction, one set of adjacent sets is shifted by 5 μm in the main scanning direction relative to the other set. When exposing one line of the photoreceptor 102, the light emission timing of the four sets is controlled so as to expose that line of the photoreceptor 102. Therefore, as shown in Figure 7, the four light-emitting elements 602, which are in approximately the same position in the main scanning direction of the four sets, expose the photoreceptor 102 at positions shifted by 5 μm each. In this way, by overlapping the spots from each light-emitting element 602, a smooth electrostatic latent image is formed. In this embodiment, the number of sets is 4, but the number of sets can be 2 or more.
[0020] As described above, the exposure head 106 of this embodiment has 20 light-emitting chips 400 arranged in a staggered pattern in two rows along the main scanning direction, and each light-emitting chip 400 has four sets of multiple light-emitting elements 602 arranged along the main scanning direction. Each set is positioned along the sub-scanning direction, and the position of one set in the main scanning direction of adjacent sets is shifted by 5 μm relative to the position of the other set in the main scanning direction with respect to a resolution of 4800 dpi. Looking at the exposure head 106 as a whole, the positions of each of the multiple light-emitting elements 602 in the main scanning direction are different. Although the positions of the multiple light-emitting elements 602 in the sub-scanning direction are not the same, the light emission timing of each light-emitting element 602 is adjusted so that they expose the same line on the photoreceptor 102. Therefore, spots from each of the multiple light-emitting elements 602 can be formed on the photoreceptor 102 at intervals of approximately 5 μm on one line in the main scanning direction. In the following description, the positions where each of the multiple light-emitting elements 602 forms a spot will be referred to as "dots". Furthermore, if the light-emitting element 602 is made to emit light at the location of the dot, the dot will be referred to as the "exposed dot," and if the light-emitting element 602 is not made to emit light at the location of the dot, the dot will be referred to as the "unexposed dot."
[0021] Figure 8 shows the control configuration of each light-emitting chip 400 by the image controller 800. The image data generation unit 801 receives image data indicating the grayscale value of each pixel of the image to be formed. The image data generation unit 801 performs dithering (halftone processing) on the image data at the resolution instructed by the CPU 811, and outputs the processed image data to the light intensity correction unit 802. The image data after halftone processing indicates whether each dot constituting the image is an exposed dot or an unexposed dot. In other words, the image data after halftone processing indicates whether or not to make the light-emitting element 602 corresponding to each dot emit light. The light intensity correction unit 802 corrects the light intensity of the image data based on the correction information, and outputs the image data after light intensity correction to the chip data conversion unit 803. The synchronization signal generation unit 804 generates a line synchronization signal (Lsync) 808. The line synchronization signal 808 is used to determine the data portion of the image data that corresponds to one line in the main scanning direction of the photoreceptor 102. The chip data conversion unit 803 transmits image data (DATA) 807 for one line to each light-emitting chip 400 in synchronization with the line synchronization signal 808. The chip select signal (CS) 805 indicates which light-emitting chip 400 the image data 807 is intended for. The chip data conversion unit 803 also transmits a clock signal (CLK) 806 to each light-emitting chip 400.
[0022] The storage section 810 of the printed circuit board 202 stores correction information, which will be described later. Each block shown in Figure 8 is configured to exchange various types of information by transmitting and receiving control signals (CTL) 809. When each light-emitting chip 400 receives image data 807 from the chip data conversion unit 803, it performs a light-emitting operation corresponding to the received image data 807 at the timing of the next line synchronization signal 808 input.
[0023] Figure 9 is a block diagram of the light-emitting chip 400. The digital-to-analog converter (D / A) 901 outputs an analog voltage corresponding to a digital value, which is a set value set by the CPU 811. This digital value is indicated in the correction information, and the CPU 811 determines the digital value to set for the D / A 901 of each light-emitting chip 400 by reading the correction information stored in the storage unit 810. The light-emitting elements 602 of the light-emitting chip 400 are grouped into multiple blocks in the main scanning direction. Each group is provided with a corresponding reference current source 902. In Figure 9, the light-emitting elements 602 are grouped into five groups, and therefore the light-emitting chip 400 has reference current sources 902-1 to 902-5 corresponding to each group. The reference current sources 902-1 to 902-5 output a reference current corresponding to the output value output by the D / A 901, i.e., the analog voltage, to each light-emitting element 602 of the corresponding group. In this manner, the D / A901 functions as a current control unit that controls the reference current to the light-emitting element 602. The amount of light emitted by the light-emitting element 602 is controlled based on the reference current output by the corresponding reference current source 902.
[0024] Figure 10 is a block diagram of the light intensity correction unit 802. Light intensity correction value A, light intensity correction value B, and spot correction value C are shown in the correction information. The CPU 811 reads the correction information stored in the storage unit 810 and notifies the light intensity correction unit 802 of light intensity correction value A, light intensity correction value B, and spot correction value C.
[0025] The light intensity correction value A is a correction value used to compensate for the difference in light intensity between groups of light-emitting chips 400. In this embodiment, since the light-emitting elements 602 within one light-emitting chip 400 are grouped into five, five light intensity correction values A are set for one light-emitting chip 400. One group, that is, one reference current source 902, is associated with one light intensity correction value A.
[0026] The light intensity correction value B is a correction value used to correct the difference in light intensity between the light-emitting elements 602 within a group. As will be described in detail later, in this embodiment, four light intensity correction values B are associated with one group of one light-emitting chip 400. For example, multiple light-emitting elements 602 that emit light with a reference current from one reference current source 902 are subgrouped into four subgroups according to their position in the main scanning direction. The light-emitting elements 602 included in one subgroup form a continuous spot in the main scanning direction. One light intensity correction value B is associated with each subgroup.
[0027] The spot correction value C is a value that indicates the amount of deviation of the spot from the reference value (hereinafter referred to as the spot deviation amount) to correct the difference in light intensity caused by the spot of the light-emitting element 602 expanding in the main scanning direction. The spot correction value C is set for each light-emitting element 602 whose spot expands. Note that light-emitting element 602 for which no spot correction value C is set is interpreted as having a spot correction value C of 0. As will be described in detail later, the effect of the spot of the light-emitting element 602 expanding in the main scanning direction differs depending on the grayscale. Specifically, when the grayscale is high, the density increases as the spot expands in the main scanning direction. Therefore, if the spot that forms the high grayscale area expands in the main scanning direction, the light intensity is reduced. On the other hand, when the grayscale is low, the density decreases as the spot expands in the main scanning direction. Therefore, if the spot that forms the low grayscale area expands in the main scanning direction, the light intensity is increased. Note that the absolute value of the increase or decrease in light intensity increases as the spot deviation amount increases.
[0028] Correction information, including light intensity correction value A, light intensity correction value B, and spot correction value C, is stored in the storage unit 810 before shipment. Furthermore, the CPU 811 can obtain light intensity correction value A, light intensity correction value B, and spot correction value C using a method described later, and update the correction information stored in the storage unit 810.
[0029] The image data processed by dithering in the image data generation unit 801 is input to the gradation determination unit 1105 and the image correction unit 1109. As described above, the image data indicates whether or not to make each light-emitting element 602 emit light when exposing each line in the main scanning direction of the photoreceptor 102.
[0030] The gradation determination unit 1105 determines the gradation value of a pixel based on the input image data and notifies the gradation correction unit 1106. The gradation correction unit 1106 has a correction table for each gradation. The correction table is included in the correction information. The correction table is a table that shows the reference light intensity correction value for each gradation. A positive reference light intensity correction value indicates an increase in light intensity, and a negative reference light intensity correction value indicates a decrease in light intensity. As described above, the effect of spot expansion in the main scanning direction differs depending on the gradation. For example, gradations are classified into three categories: low gradation, medium gradation, and high gradation, based on a first threshold and a second threshold. The first threshold is greater than the second threshold, high gradation values are greater than the first threshold, low gradation values are less than the second threshold, and medium gradation values are greater than or equal to the second threshold and less than or equal to the first threshold. The reference light intensity correction values shown in the correction table are positive for low tonal ranges, negative for high tonal ranges, and 0 for medium tonal ranges. In other words, a negative reference light intensity correction value is 0 for low and medium tonal ranges, and a positive reference light intensity correction value is 0 for high and medium tonal ranges.
[0031] The tone correction unit 1106 corrects the reference light intensity correction value of the tone of a pixel notified by the tone determination unit 1105 based on the spot shift amount indicated by the spot correction value C of the light-emitting element 602 that forms the dot constituting the pixel, and obtains the light intensity correction value D of that dot. For example, the tone correction unit 1106 holds coefficient information that shows the correspondence between the spot shift amount and a coefficient, and obtains the light intensity correction value D by multiplying the reference light intensity correction value of the tone notified by the tone determination unit 1105 by the coefficient corresponding to the spot shift amount. Note that the light intensity correction value D of dots formed by light-emitting elements 602 for which no spot correction value C is set, that is, light-emitting elements 602 for which the spot correction value C is 0, is always 0. The tone correction unit 1106 outputs data indicating the light intensity correction value D of each dot constituting the image to the image correction unit 1109.
[0032] The calculation unit 1107 determines the light intensity correction value E for each light-emitting element 602, which is positioned at different locations in the main scanning direction, based on the light intensity correction value A and the light intensity correction value B. The light intensity correction value E for a light-emitting element 602 is the sum of the light intensity correction value A for the group to which the light-emitting element 602 belongs and the light intensity correction value B for the subgroup to which the light-emitting element 602 belongs. As will be described in detail later, the sum of the light intensity correction value A for the group to which the light-emitting element 602 belongs and the light intensity correction value B for the subgroup to which the light-emitting element 602 belongs is 0 or a negative value and cannot be a positive value. In other words, the value of this sum indicates that the light intensity will remain the same or decrease, and does not indicate that the light intensity will increase. The light intensity correction value E is also the correction value for the light intensity of each dot on one line in the main scanning direction, which is formed by each light-emitting element 602 positioned at different locations in the main scanning direction. The calculation unit 1107 outputs the light intensity correction value E for each dot on one line in the main scanning direction to the image correction unit 1109.
[0033] The image correction unit 1109 divides the data representing the light intensity correction value D of each dot constituting the image into first data representing the light intensity correction value D of dots that increase the light intensity, and second data representing the light intensity correction value D of dots that decrease the light intensity. The image correction unit 1109 also generates third data representing the light intensity correction value E of each dot constituting the image based on the light intensity correction value E of each dot in one line in the main scanning direction. The image correction unit 1109 then adds the absolute values of the light intensity correction value D and the light intensity correction value E of the same dots in the second and third data to generate fourth data representing the total light intensity correction value of each dot constituting the image. The total light intensity correction value of each dot shown in the fourth data indicates that the amount of decrease in light intensity is 0 or greater, and will be referred to as subtraction data below. On the other hand, the light intensity correction value D of each dot shown in the first data indicates that the amount of increase in light intensity is 0 or greater, and will be referred to as addition data below. The image correction unit 1109 corrects the image data based on the subtraction data and the addition data. In this embodiment, the image correction unit 1109 performs image correction in units of partial images of a predetermined size, which are a part of the image to be formed. In this example, the size of the partial image is 10 × 10 pixels (100 pixels in total). Figure 11(A) shows an example of a partial image of a 10 × 10 pixel portion of the image formed from the image data before correction. In Figure 11(A), one square represents one pixel. Shaded pixels indicate pixels to which toner will adhere, and white pixels indicate pixels to which toner will not adhere.
[0034] In this embodiment, one pixel is formed by 10 consecutive dots in both the main scanning direction and the sub-scanning direction. Figure 11(B) shows an example of image data for forming one pixel in Figure 11(A). Hereinafter, the 10 light-emitting elements 602 in the main scanning direction that form one pixel in Figure 11(B) will be denoted as light-emitting elements #1 to #10. The K-th (K is an integer from 1 to 10) square from the left in Figure 11(B) indicates a dot (spot) by light-emitting element #K. Specifically, a shaded square indicates an exposed dot, meaning that light-emitting element #K emits light, while a white square indicates an unexposed dot, meaning that light-emitting element #K does not emit light. The vertical direction in Figure 11(B) corresponds to the position in the sub-scanning direction. For example, light-emitting element #1 is shown to emit light at the 1st to 4th, 7th, and 8th formation positions of the 10 dots in the sub-scanning direction. Figure 11(B) can be considered to show whether each of the 10x10 dots forming a single pixel is an exposed dot or an unexposed dot.
[0035] In the following, the dots (spots) shown in Figures 11(B) to 11(D) will be identified by numbers in the main scanning direction and the sub-scanning direction. In the main scanning direction, the leftmost dot is numbered 1, and the rightmost dot is numbered 10. In the sub-scanning direction, the uppermost dot is numbered 1, and the lowermost dot is numbered 10. For example, the second dot in the main scanning direction and the third dot in the sub-scanning direction will be denoted as (2,3).
[0036] The image correction unit 1109 has a threshold matrix table for subtraction and a threshold matrix table for addition. The threshold matrix table is a table that shows the thresholds for 10 × 10 pixels, that is, 100 × 100 dots, to be corrected. The image correction unit 1109 compares the absolute value of the total light intensity correction value of the dots corresponding to the partial image among the dots of the image indicated by the subtraction data with the threshold of the corresponding dot indicated by the subtraction threshold matrix table. Then, the image correction unit 1109 determines a dot as a first modified dot if the absolute value of the total light intensity correction value exceeds the threshold in the subtraction threshold matrix table.
[0037] Figure 11(C) shows an example of the determination result using a threshold matrix table for subtraction of a single pixel portion corresponding to Figure 11(B). In Figure 11(C), the dots at positions (4,2), (7,5), (2,8), and (8,10) are determined to be first modified dots. If the first modified dot is an exposed dot, the image correction unit 1109 changes it to an unexposed dot. On the other hand, if the first modified dot is an unexposed dot, the image correction unit 1109 leaves it as an unexposed dot. Therefore, the image correction unit 1109 corrects the image data of Figure 11(B) as shown in Figure 11(D). The dot at position (4,2) in Figure 11(B) was originally an unexposed dot, and therefore remains an unexposed dot after correction. Meanwhile, the dots at positions (7,5), (2,8), and (8,10) are corrected from exposed dots to unexposed dots.
[0038] The image correction unit 1109 similarly uses the summation data and the threshold matrix table for summation to determine the second modified dot. If the second modified dot is an unexposed dot, the image correction unit 1109 changes the second modified dot to an exposed dot. On the other hand, if the second modified dot is an exposed dot, the image correction unit 1109 leaves the second modified dot as an exposed dot. If the same dot is selected as both the first modified dot and the second modified dot, the image correction unit 1109 does not change the exposure / unexposure status of the dot, leaving it in the state indicated by the original image data. The threshold matrix table can be one with high spatial frequency characteristics, commonly used in the Blue noise mask method.
[0039] The threshold matrix table (100 x 100 dots in this example) is used repeatedly in both the main and sub-scan directions. However, since the subtraction and addition data being compared are applied to the entire image and not repeated at any particular interval, the occurrence of image defects at processing boundaries can be suppressed. The thresholds in the threshold matrix table are set so that the spacing between the first and second modification dots is not uniform. By making the spacing between the first and second modification dots non-uniform, the occurrence of moiré patterns can be prevented.
[0040] Furthermore, by making the correction resolution sufficiently fine relative to the pixel size of the original image data, it becomes possible to correct the light intensity with high precision. In addition, by performing the light intensity correction before the chip data conversion unit 803 divides the image data for each light-emitting chip 400, it is possible to suppress the occurrence of image defects at the boundaries of the light-emitting chips 400 compared to a configuration in which the light intensity correction is performed after division.
[0041] In this embodiment, the exposure / non-exposure of dots obtained by dividing a single pixel shown in the image data is corrected in units of a partial image of a predetermined area (10 × 10 pixels in this example). This configuration allows for simple and highly accurate correction compared to performing light intensity correction using complex analog circuits. Furthermore, by performing light intensity correction based on the light intensity correction value of each light-emitting element 602 that forms a spot continuously in the main scanning direction, that is, the light intensity correction value at each position continuous in the main scanning direction, the occurrence of image defects can be prevented. In addition, by performing light intensity correction in units of dots obtained by dividing a single pixel, high-precision light intensity correction can be achieved.
[0042] In this embodiment, the light intensity fluctuation of each light-emitting element 602 in the main scanning direction is corrected in two stages. First, as the first stage of correction, the light intensity fluctuation between light-emitting chips 400 is corrected by adjusting the digital value set in the D / A901 of the light-emitting chip 400. In order to determine the digital value set in the D / A901 of each light-emitting chip 400, all light-emitting elements 602 within the light-emitting chip 400 are lit up and the light intensity value of each light-emitting element 602 in the light-emitting chip 400 is measured. Then, the digital value set in the D / A901 is determined so that the light intensity of the light-emitting element 602 with the lowest light intensity within the light-emitting chip 400 becomes the target light intensity. Therefore, the light intensity of all light-emitting elements 602 within the light-emitting chip 400 becomes equal to or greater than the target light intensity. Therefore, as described above, the light intensity correction value E for each light-emitting element will be a value that indicates whether the light intensity remains the same or is reduced. By performing the first stage of light intensity correction using the digital value set in the D / A901, the amount of correction in the light intensity correction unit 802 can be reduced, and thus the deterioration of image quality due to image data correction can be suppressed.
[0043] The second stage of correction involves correcting light intensity fluctuations within the light-emitting chip 400, and as described above, this is performed by the light intensity correction unit 802 correcting the image data. The light intensity correction values A, B, and C used by the light intensity correction unit 802, and the digital values input to the D / A901 of each light-emitting chip 400 are generated based on the measurement results in the assembly and adjustment process of the exposure head 106 and stored in the storage unit 810 as correction information. The CPU 811 reads the correction information and sets the light intensity correction values A, B, and C in the light intensity correction unit 802, and also sets the digital values in the D / A901 of each light-emitting chip 400.
[0044] The spot correction value C indicates the amount of deviation of the spot from the reference value (spot deviation). To measure the spot correction value C, each light-emitting element 602 is made to emit light individually. The spot size is then measured by reading the spot with a CCD camera, and the amount of change from the reference value is measured. The relationship between the location of occurrence, i.e., the light-emitting element 602, is defined as the spot correction value C.
[0045] Correction information can be generated within the image forming apparatus. Figure 12 shows a light intensity correction chart, which is a measurement image formed on a sheet to generate correction information. The light intensity correction chart is formed by the image forming apparatus in response to a user instruction to perform light intensity uniformity adjustment. The user has the reading unit 100 read the sheet on which the light intensity correction chart has been formed. As a result, the CPU 811 acquires chart data, which is the reading result from the reading unit 100. The chart data is data showing the density distribution in the main scanning direction for each of the multiple grayscale images 2101 to 2106.
[0046] The light intensity correction chart has multiple grayscale images 2101 to 2106 that form a band in the main scanning direction, and reference marks 2111-1 to 2119-19 and 2112-1 to 2112-19 positioned above and below the grayscale images 2101 to 2106. Each reference mark is a marker image for identifying the position of each light-emitting chip 400, and is formed by the light emission of light-emitting elements 602 at the ends of each light-emitting chip 400 in the main scanning direction. For example, reference mark 2111-2 is formed by the light emission of four light-emitting elements 602 at the right end of light-emitting chip 400-2 and four light-emitting elements 602 at the left end of light-emitting chip 400-3. The CPU 811 determines each reference mark based on the chart data. The CPU 811 then determines the regions formed by light-emitting chips 400-1 to 400-20 for each of the grayscale images 2101 to 2106, based on the lines connecting the reference mark 2111-p (where p is an integer from 1 to 19) and the reference mark 2112-p. For example, region B1 in Figure 12 is determined to have been formed by light-emitting chip 400-2. The left edge of Figure 12 is determined to have been formed by light-emitting chip 400-1, and the right edge of Figure 12 is determined to have been formed by light-emitting chip 400-20.
[0047] The sets of grayscale images 2101 and 2102 are formed using image data with the same grayscale values. However, when forming grayscale image 2102, the CPU 811 sets the digital value set in the D / A 901 of each light-emitting chip 400 to be lower by a predetermined ratio than the digital value set in the D / A 901 of each light-emitting chip 400 when forming grayscale image 2101. Therefore, the density of grayscale image 2102 is lower than the density of grayscale image 2101. The same applies to the sets of grayscale images 2103 and 2104 and the sets of grayscale images 2105 and 2106. Note that the grayscale values shown by the image data used to form the sets of grayscale images 2101 and 2102, the sets of grayscale images 2103 and 2104, and the sets of grayscale images 2105 and 2106 are different. Specifically, the tonal values shown by the image data when forming the set of tonal images 2101 and 2102 are set to be the highest, and the tonal values shown by the image data when forming the set of tonal images 2105 and 2106 are set to be the lowest. The density of tonal image 2102 is higher than the density of tonal image 2103, and the density of tonal image 2104 is higher than the density of tonal image 2105.
[0048] Next, the method for converting the chart data read by the reading unit 100 into light intensity data will be explained using Figure 13. For each of the grayscale images 2101 to 2016, the CPU 811 calculates the average density 2101_D to 2106_D by averaging the read density at each position in the main scanning direction. Figure 13 shows the relationship between the digital value set in D / A901 when forming each of the grayscale images 2101 to 2106 and the average density 2101_D to 2106_D. For the grayscale images 2101 and 2102, the CPU 811 calculates the amount of change k1 in the digital value in response to the change in density. Specifically, the CPU 811 calculates the amount of change k1 by dividing the difference in the digital value set in D / A901 when forming grayscale images 2101 and 2102 by the difference between the average density 2101_D and the average density 2102_D. Similarly, CPU 811 calculates the change amount k2 for the set of grayscale images 2103 and 2104, and the change amount k3 for the set of grayscale images 2104 and 21054.
[0049] The CPU 811 determines the light intensity distribution of the grayscale image 2101 in the main scanning direction by multiplying the density at each position in the main scanning direction of the grayscale image 2101, which is determined based on the chart data, by the slope k1. Similarly, the CPU 811 also determines the light intensity distribution in the main scanning direction for grayscale images 2103 and 2105. Note that instead of changing the digital value set in the D / A 901, the light intensity distribution can also be determined by changing the grayscale of the image data used to form grayscale images 2101 and 2102.
[0050] In this embodiment, the CPU 811 determines the digital value to be set for D / A901, as well as light intensity correction values A and B, based on the light intensity distribution of the grayscale image 2103, which is an image in the intermediate density region. The CPU 811 also determines the spot correction value C based on the light intensity distribution of the grayscale image 2101 in the high density region and the grayscale image 2105 in the low density region. The method for determining the digital value to be set for D / A901, as well as light intensity correction values A and B, will be explained below using Figure 14.
[0051] Figure 14 shows the light intensity distribution of the grayscale image 2103. Note that Figure 14 shows only the portion corresponding to one light-emitting chip 400. Which part of the grayscale image 2103 was formed by which light-emitting chip 400 can be determined by the reference marks, as explained using Figure 12. The CPU 811 determines the digital value to set in the D / A 901 so that the lowest light intensity in Figure 14 becomes the target light intensity T (target value). Specifically, the CPU 811 determines the digital value to set in the D / A 901 by increasing the digital value set in the D / A 901 when forming the grayscale image 2103 by a digital value corresponding to the value obtained by subtracting the lowest light intensity in Figure 14 from the target light intensity T.
[0052] The light intensity 2301 in Figure 14 is the light intensity at a predetermined position within the range in which a dot is formed by multiple light-emitting elements 602 in the group corresponding to the reference current source 902-1. Similarly, the light intensity values 2302 to 2305 are the light intensity at predetermined positions within the range in which a dot is formed by multiple light-emitting elements 602 in the groups corresponding to the reference current sources 902-2 to 902-5, respectively. The CPU 811 sets the difference between light intensity 2301 and the lowest light intensity in Figure 14 as the light intensity correction value A associated with the reference current source 902-1. As mentioned above, the lowest light intensity in Figure 14 becomes the target light intensity T depending on the digital value set in D / A 901. The CPU 811 similarly determines the light intensity correction values A associated with the reference current sources 902-2 to 902-5.
[0053] Furthermore, the CPU 811 determines the light intensity at four positions within the range where dots are formed by multiple light-emitting elements 602 in a group corresponding to the reference current source 902-1. The positions for determining the light intensity are selected from within the range where dots are formed by multiple light-emitting elements 602 in one subgroup. The CPU 811 takes the difference between each of the four determined light intensity values and the light intensity 2301 as the light intensity correction value B associated with each subgroup of the reference current source 902-1. The CPU 811 similarly determines the light intensity correction values B associated with reference current sources 902-2 to 902-5.
[0054] In this way, the entire group of light-emitting elements 602 is corrected using a light intensity correction value A, which is based on the reference current source 902, and the light intensity fluctuations of the light-emitting elements 602 within the group are corrected using a light intensity correction value B. With this configuration, the light intensity correction value B can be represented with a small number of bits, reducing the amount of data for the correction information. For example, the light intensity correction value A can be represented with 4 bits, and the light intensity fluctuations within the group, i.e., the light intensity correction value B representing the residual component, can be represented with 2 bits.
[0055] Next, we will explain how to determine the spot correction value C. Figure 15(A) shows the light intensity distribution of grayscale images 2101, 2103, and 2105. Note that Figure 15(A) displays the light intensity of each grayscale image 2101, 2103, and 2105 after normalization. Specifically, for grayscale image 2101, the value on the vertical axis of Figure 15 is obtained by dividing the light intensity at each position in the main scanning direction of grayscale image 2101 by the average light intensity of grayscale image 2101. The same applies to grayscale images 2103 and 2105. Because it is normalized, the light intensity of grayscale images 2101, 2103, and 2105 is similar at most positions in the main scanning direction.
[0056] However, due to manufacturing variations in the exposure head 106, the spot size of the light-emitting element 602 changes locally, resulting in different light intensities for the grayscale images 2101, 2103, and 2105. Specifically, in the case of the low-gradation grayscale image 2105, if the spot size increases locally, sufficient light intensity cannot be obtained, and the density decreases. In other words, in terms of light intensity, the light intensity decreases as shown by reference numeral 2307 in Figure 15(A). On the other hand, in the case of the high-gradation grayscale image 2101, the density increases due to the blurring of the spaces between adjacent pixels. In other words, in terms of light intensity, the light intensity increases as shown by reference numeral 2306 in Figure 15(A). Reference numeral 2308 in Figure 15(A) indicates the light intensity of the medium-gradation grayscale image 2103.
[0057] The solid line in Figure 15(B) shows the density characteristics when there is no change in spot size, while the dotted line shows the density characteristics when the spot size exceeds the reference size. As shown in Figure 15(B), when the spot size exceeds the reference size, the density increases in the high-tone region and decreases in the low-tone region. The effect in the mid-tone region is small.
[0058] The CPU 811 calculates the peak value difference, which is the difference between the normalized peak light intensity of the grayscale image 2101 (reference numeral 2306 in Figure 15(A)) and the normalized peak light intensity of the grayscale image 2105 (reference numeral 2307 in Figure 15(A)). The image forming apparatus stores judgment information in advance that shows the relationship between the experimentally determined peak value difference and the spot shift amount. Using the judgment information based on the calculated peak value difference, the CPU 811 calculates a spot correction value C associated with the light-emitting element 602 corresponding to the position in the main scanning direction where the normalized light intensity is fluctuating.
[0059] The specific values used in describing this embodiment are illustrative, and the present invention is not limited to using these specific values.
[0060] In this embodiment, the light intensity fluctuations of each light-emitting element 602 in the main scanning direction are corrected in two stages. First, the image controller 800 corrects the light intensity difference between the light-emitting chips 400 using a digital value set in the D / A 901 within the light-emitting chip 400. Then, the image controller 800 corrects the light intensity fluctuations of each light-emitting element 602 within the light-emitting chip 400 by correcting the image data. By correcting the light intensity difference between the light-emitting chips 400 using a digital value set in the D / A 901 within the light-emitting chip 400, the amount of image data correction can be reduced, and the degradation of image quality due to image data correction can be suppressed. Furthermore, by correcting the light intensity difference of the light-emitting elements 602 within the light-emitting chip 400 using image data correction, correction can be performed simply and with high accuracy compared to a configuration in which a correction circuit is provided to individually correct the current flowing through each light-emitting element 602. In other words, with the configuration of this embodiment, density unevenness can be suppressed without increasing the circuit size compared to a case in which a correction circuit for correcting the current flowing through each light-emitting element 602 within the light-emitting chip 400 is provided on the chip.
[0061] Furthermore, image data correction is performed on a partial image basis, by changing the exposed and unexposed dots using a threshold matrix of the same size as the partial image. The same threshold matrix is repeatedly used for each partial image that makes up the image. However, the light intensity correction value compared with the threshold matrix is for the entire image and is independent of the size of the threshold matrix, so it is possible to suppress the occurrence of image defects at the boundaries of partial images. In addition, since the exposure / unexposed dots are changed on a unit basis of multiple dots that make up one pixel, light intensity correction can be performed with high precision.
[0062] [Other embodiments] The present invention can also be realized by supplying a program that implements one or more of the functions of the above-described embodiments to a system or device via a network or storage medium, and by having one or more processors in the computer of that system or device read and execute the program. It can also be realized by a circuit (e.g., an ASIC) that implements one or more functions.
[0063] The invention is not limited to the embodiments described above, and various modifications and variations are possible without departing from the spirit and scope of the invention. Accordingly, claims are attached to disclose the scope of the invention. [Explanation of Symbols]
[0064] 106: Exposure head, 400-1~400-20: Light-emitting chip, 602: Light-emitting element, 801: Image data correction unit, 802: Light intensity correction unit, 803: Data conversion unit, 811: CPU
Claims
1. An image forming apparatus for forming an image on a sheet, A photoconductor; an exposure head including a plurality of light-emitting chips arranged at different positions in a main scanning direction, each of the plurality of light-emitting chips having a plurality of light-emitting elements arranged at different positions in the main scanning direction and a current control means for controlling a current flowing through the plurality of light-emitting elements based on a set value, and forming an electrostatic latent image on the photosensitive member by repeatedly exposing one line in the main scanning direction of the photosensitive member that is rotated and driven by the plurality of light-emitting elements of each of the plurality of light-emitting chips based on image data; a developing means for developing the electrostatic latent image on the photoconductor to form an image on the photoconductor; a correction means for suppressing unevenness in the amount of light from the exposure head; Equipped with The image forming apparatus according to the present invention, characterized in that the correction means suppresses unevenness in the amount of light from the exposure head by correcting the image data and by setting the setting value for the current control means for each of the plurality of light-emitting chips.
2. The image forming apparatus described in claim 1, characterized in that the correction means sets the setting value of the current control means of each of the plurality of light-emitting chips so that the light amount of the light-emitting element with the lowest light amount among the plurality of light-emitting elements included in the light-emitting chip becomes the target light amount.
3. The image forming apparatus according to claim 2, characterized in that the correction means corrects the image data for each of the plurality of light-emitting chips based on first correction information for determining a first light intensity correction value of each of the plurality of light-emitting elements included in the light-emitting chip.
4. the image data indicates, for each of the plurality of dots constituting the image, whether the dot is an exposure dot that is exposed by each of the plurality of light-emitting elements included in each of the plurality of light-emitting chips, or a non-exposure dot that is not exposed; The image forming apparatus described in claim 3, characterized in that the correction means selects a first change dot from the plurality of dots based on a first light intensity correction value of each of the plurality of light-emitting elements included in each of the plurality of light-emitting chips, and when the first change dot is the exposed dot, corrects the image data by changing the first change dot to the non-exposed dot.
5. The plurality of light emitting elements included in each of the plurality of light emitting chips are grouped into a plurality of groups each including a plurality of first light emitting elements; The first light emitting elements included in each of the groups are subgrouped into a plurality of subgroups including a plurality of second light emitting elements; 5 . The image forming apparatus according to claim 3 , wherein the first correction information includes a first correction value for each of the plurality of groups, and a second correction value for each of the plurality of subgroups of each of the plurality of groups.
6. Each of the plurality of light emitting chips has a current source corresponding to each of the plurality of groups, The image forming device described in claim 5, characterized in that the current source included in the light-emitting chip supplies current to each of the multiple first light-emitting elements included in the corresponding group based on an output value output by the current control means included in the light-emitting chip in accordance with the set value.
7. the first correction value of the group is a difference between a first light amount among light amounts indicated by a light amount distribution in the main scanning direction of the plurality of first light-emitting elements included in the group when the plurality of first light-emitting elements are caused to emit light, and the target light amount; The image forming apparatus according to claim 5 or 6, characterized in that the second correction value of a subgroup within the group is the difference between a second light amount and the first light amount in the light amount distribution in the main scanning direction of the multiple second light-emitting elements included in the subgroup when the multiple second light-emitting elements are made to emit light.
8. The image forming apparatus described in claim 3, characterized in that the correction means corrects the image data for each of the multiple light-emitting chips based further on second correction information indicating the amount of deviation from a reference value of the size of the light spot on the photosensitive body caused by each of the multiple light-emitting elements included in the light-emitting chip.
9. the image data indicates, for each of the plurality of dots constituting the image, whether the dot is an exposure dot that is exposed by each of the plurality of light-emitting elements included in each of the plurality of light-emitting chips, or a non-exposure dot that is not exposed; The correction means is a determination means for determining a gradation value of a pixel formed by each of a plurality of first dots related to the formation of each of the plurality of light-emitting elements included in a light-emitting chip based on the image data, and determining a second light quantity correction value of each of the plurality of first dots based on the deviation amount and the gradation value of each of the plurality of light-emitting elements included in the light-emitting chip; a generating means for generating a fourth light amount correction value for each of the first dots based on a third light amount correction value indicating a reduction in a light amount among the second light amount correction values for each of the first dots and a first light amount correction value of a light emitting element involved in forming the first dots; Equipped with The image forming apparatus of claim 8, wherein the correction means corrects the image data by selecting a first change dot from among the plurality of first dots based on the fourth light amount correction value of each of the plurality of first dots, and if the first change dot is the exposed dot, changing the first change dot to the non-exposed dot, selecting a second change dot from among the plurality of first dots based on a fifth light amount correction value indicating an increase in the amount of light among the second light amount correction values of each of the plurality of first dots, and if the second change dot is the non-exposed dot, changing the second change dot to the exposed dot.
10. 10. The image forming apparatus according to claim 9, wherein when the same first dot is selected as the first change dot and the second change dot, the correction unit does not change the first dot.
11. When the gradation value is greater than the first threshold, the second light amount correction value indicates 0 or a reduction in the amount of light; When the gradation value is smaller than the second threshold value, the second light amount correction value indicates 0 or an increase in the amount of light; 11. The image forming apparatus according to claim 9, wherein the first threshold value is greater than the second threshold value.
12. The correction means is a forming means for forming a measurement image on the sheet, the measurement image including a first image and a second image for measuring a first light amount distribution in the main scanning direction of the exposure head; a reading means for reading the measurement image formed on the sheet; Equipped with the correction means determines the setting value to be set in the current control means of each of the plurality of light-emitting chips based on the reading result of the reading means, and generates the first correction information for each of the plurality of light-emitting chips; An image forming apparatus as described in any one of claims 8 to 11, characterized in that the forming means sets a first setting value in the current control means of each of the multiple light-emitting chips when forming the first image, which is different from a second setting value set in the current control means of each of the multiple light-emitting chips when forming the second image.
13. 13. The image forming apparatus according to claim 12, wherein the forming means makes a first gradation value of the image data when forming the first image equal to a second gradation value of the image data when forming the second image.
14. The image forming apparatus according to claim 13, characterized in that the correction means determines the first light quantity distribution from the density distribution in the main scanning direction of the first image based on the ratio of the difference between the average density of the first image and the average density of the second image and the difference between the first set value and the second set value.
15. the measurement image includes a marker image for determining an area formed by each of the plurality of light-emitting chips included in the exposure head for each of the first image and the second image, An image forming apparatus as described in any one of claims 12 to 14, characterized in that the setting value set in the current control means of the light-emitting chip is a value that sets the target light amount to the lowest first light amount among the light amounts indicated by the second light amount distribution, which is the portion of the first light amount distribution of the exposure head that corresponds to the light-emitting chip.
16. The image forming apparatus according to claim 15 , wherein the first correction information of the light emitting chip is information for determining a difference between a plurality of light amounts indicated by the second light amount distribution and the first light amount.
17. 17. An image forming apparatus according to claim 15 or 16, wherein the marker image is formed by a light-emitting element arranged at an end in the main scanning direction among the plurality of light-emitting elements included in each of the plurality of light-emitting chips.
18. the measurement images further include a third image, a fourth image, a fifth image, and a sixth image; the forming means makes a third setting value set in the current control means of each of the plurality of light-emitting chips when forming the third image different from a fourth setting value set in the current control means of each of the plurality of light-emitting chips when forming the fourth image, makes a fifth setting value set in the current control means of each of the plurality of light-emitting chips when forming the fifth image different from a sixth setting value set in the current control means of each of the plurality of light-emitting chips when forming the sixth image, makes a third gradation value of the image data when forming the third image equal to a fourth gradation value of the image data when forming the fourth image, and makes a fifth gradation value of the image data when forming the fifth image equal to a sixth gradation value of the image data when forming the sixth image, The image forming apparatus of claim 13, wherein the correction means determines a second light amount distribution in the main scanning direction of the exposure head from the density distribution in the main scanning direction of the third image based on a ratio of a difference between an average density of the third image and an average density of the fourth image and a difference between the third set value and the fourth set value, determines a third light amount distribution in the main scanning direction of the exposure head from the density distribution in the main scanning direction of the fifth image based on a ratio of a difference between an average density of the fifth image and an average density of the sixth image and a difference between the fifth set value and the sixth set value, and generates the second correction information by comparing the second light amount distribution with the third light amount distribution.
19. 20. The image forming apparatus according to claim 18, wherein the third gradation value is greater than the first gradation value, and the fifth gradation value is less than the first gradation value.