JP2006088507A - Image forming apparatus - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an image forming apparatus exhibiting excellent gradation reproducibility for an original image by shortening the time required for rewriting a look-up table. <P>SOLUTION: The image forming apparatus comprises a look-up table 44, an output control section 42 for controlling laser light to produce an laser output dependent on the gray level of an image with reference to the look-up table 44, and a control section 20 for rewriting the look-up table 42 wherein the control section 20 rewrites the look-up table 44 by performing linear interpolation of the look-up table 44 defined discretely through digital differential analysis. Operation can be simplified and processing time can be shortened. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to an image forming apparatus that faithfully forms an image read by a scanner or the like or an image created by a personal computer or the like. In particular, the present invention relates to output control of a laser writing device that writes an electrostatic latent image on a photosensitive drum.

  The laser writing device irradiates a laser beam with an intensity corresponding to the gray value of the pixel to form an electrostatic latent image on the photosensitive member. There are various factors between the intensity of the laser beam and the amount of potential change on the photoconductor, depending on the laser modulation method and the material of the photoconductor. However, the stronger the laser beam, the more the potential change on the photoconductor. Has a relationship of growing. However, this relationship is affected by variable factors such as the environmental quantity such as humidity, the degree of wear of the photoconductor, and the aging of the charger.

  In addition, since the laser writing device has a laser diode as a component, the relationship between the output intensity instructed by the image processing means to the laser output mechanism and the laser output that is actually output is also affected by changes in temperature and laser diode over time Affected by.

  As described above, the relationship between the gray value designated by the image processing means and the corresponding potential on the electrostatic latent image constantly fluctuates and is not constant. However, the potential of the electrostatic latent image is a main parameter that determines the image density of the image to be developed. To accurately reproduce the gray value of the image acquired by the image acquisition means to the image density, It is necessary to always maintain an appropriate relationship between the electric potentials of the electrostatic latent images.

  For this reason, control is performed to actually irradiate the photoconductor with laser light having a reference intensity, measure the electric potential on the photoconductor, and feed back to the laser light intensity.

  Patent Documents 1 and 2 propose an image processing apparatus that achieves high-speed processing.

JP-A-11-167627 JP 2003-346140 A

  However, although the processing capability of recent CPUs has been remarkably improved, many CPUs that are mounted on image forming apparatuses have extremely low processing capability for cost reasons. For this reason, there is a problem that the processing load is extremely heavy for operations that require repeated multiplication and division.

  Further, Patent Documents 1 and 2 described above do not describe a technique for efficiently performing an interpolation process.

  The present invention has been made in view of the above circumstances, and an object thereof is to provide an image forming apparatus that reduces the processing load and shortens the processing time.

  In order to achieve such an object, an image forming apparatus of the present invention includes a look-up table, a laser writing unit that refers to the look-up table, and controls laser light so as to obtain a laser output corresponding to the gray value of the image. And the rewriting means for rewriting the look-up table by linearly interpolating the discretely defined look-up table by a digital differential analysis method. Since the discretely defined lookup table is linearly interpolated by the digital differential analysis method, the calculation can be simplified and the processing time can be shortened.

  In the image forming apparatus having the above-described configuration, the rewriting unit may round off the decimal point when linearly interpolating the discretely defined lookup table. More accurate gradation controllability can be obtained.

  In the image forming apparatus configured as described above, the rewriting unit may rewrite the lookup table by performing Bezier interpolation on the discretely defined lookup table. Therefore, the calculation can be simplified and the processing time can be shortened.

  In the image forming apparatus configured as described above, the image forming apparatus includes a photosensitive member and a sensor capable of measuring a potential on the photosensitive member, and the lookup table is updated based on the potential on the photosensitive member. Good.

  In the image forming apparatus having the above configuration, the image forming apparatus includes an intermediate transfer member and a sensor capable of measuring the density of the toner transferred onto the intermediate transfer member, and the lookup table is updated by the intermediate transfer member. It may be performed based on the toner density transferred above.

  In the image forming apparatus configured as described above, the image forming apparatus includes a printing mechanism for paper and a sensor capable of measuring the output image density printed on the paper, and the update of the lookup table is printed. It may be performed based on the output image density.

  In the image forming apparatus configured as described above, the sensor capable of measuring the output image density may be an image scanner capable of reading an image serving as a document.

  The present invention can provide an image forming apparatus that shortens the time required for rewriting the look-up table and has excellent gradation reproducibility with respect to the original image.

  The best embodiment of the present invention will be described with reference to the accompanying drawings.

  First, the configuration of the present embodiment will be described with reference to FIG. In FIG. 1, a document 2 placed on a document table 1 is R (red) and G (green) by an image scanner including a color CCD sensor 3 via a scanning optical system including a light source and a scanning mirror. , B (blue) analog image signals. The analog image signals of R, G, and B read by the color CCD sensor 3 are converted into Y (yellow), M (magenta), C (cyan), and K (black) image images by the image processing unit 4. Image data of each color is sequentially output to ROS (Raster Output Scanner) 7C, 7M, 7Y, 7K of the forming units 5C, 5M, 5Y, 5K, and emitted from these ROS 7C, 7M, 7Y, 7K according to the image data. Laser beams are scanned and exposed on the surfaces of the respective photoconductive drums 6C, 6M, 6Y, and 6K to form electrostatic latent images. The electrostatic latent images formed on the photosensitive drums 6C, 6M, 6Y, and 6K are developed as toner images of respective colors Y, M, C, and K by the developing devices 8C, 8M, 8Y, and 8K, respectively.

  In addition, the image processing unit 4 decomposes the image into two-dimensionally arranged pixels as shown in FIG. A laser output control unit 42 for controlling the writing output of the light source, and a gray value replacement unit 43 for rewriting the look-up table 44 with values obtained by the control unit 20.

  FIG. 3 shows a configuration of the control unit 20 that controls each functional unit described above. The program is composed of a ROM 23 that stores a program, a RAM 22 that is used for processing, and a CPU 21 that controls the entire image forming apparatus 1. The CPU 21 performs control to actually irradiate the photosensitive drum 2 with a laser beam having a reference intensity, measure the potential on the photosensitive member, and feed back to the laser beam intensity. This control is realized by the CPU 21 performing an operation according to the program recorded in the RAM 22.

  Each functional unit is connected via the control unit 20 and the I / O unit 24. The I / O unit is connected to the image processing unit 4, developing device 8, ROS 7, power supply circuit 31, potential sensor 32, toner density sensor 33, image scanner 34, and the like. The potential sensor 32 is a sensor that can measure the potential on the photosensitive drum 2, and the look-up table 44 can be updated based on the potential on the photosensitive member.

  The toner density sensor 33 is a sensor capable of measuring the toner density transferred onto the intermediate transfer body, and the lookup table 44 is updated based on the toner density transferred onto the intermediate transfer body. You can also.

  The image scanner 34 measures the output image density printed on the printing paper. The lookup table 44 can also be updated based on the printed output image density.

  In general, control aiming at accurate reproduction of gray values is called gradation reproduction control, and feedback control is a kind of gradation reproduction control. Therefore, it is conceivable to appropriately replace the gray value obtained by the raster processing means and set the output as the image processing means to the value after replacement. This process is called a gray value replacement process, and the gray value replacement process can be realized by a replacement table called a lookup table. The gradation reproduction control shown in this embodiment is appropriately changed by changing the contents of the lookup table. Can be implemented.

  This control can be expressed formally as follows. The output intensity instructed by the image processing unit 4 to the ROS 7 is x, the ideal potential on the photoreceptor corresponding to the gray value x instructed by the image processing unit 4 is f (x), and on the actual photoreceptor corresponding to x Is assumed to be g (x). As described above, g (x) is not only x but also a function of change over time and environment. Now, suppose there is a gray value replacement x '= R (x) that maps x to another gray value by a lookup table, and f (x) = g (R (x)) holds for all x If R (x) can be obtained, the ideal intensity of the latent image can be obtained under the actual photoreceptor characteristics by replacing the output intensity x in the raster processing means once as x ′ = R (x). Image potential characteristics can be achieved.

Here, the lookup table R (x) that realizes the gray value replacement can be defined as R (x) = g ⁻¹ (f (x)) by definition. Since g (x) and g ^-1 (x) are functions that can only be known by actual measurement, as described above, the photoconductor is actually irradiated while changing the intensity x of the laser beam, and the potential on the photoconductor is measured. Must be measured with a potential sensor to obtain g (x). However, the measurement of the potential is a relatively time-consuming process, and it is not practical to obtain g (x) for all possible x.

For this reason, several points are selected as representative laser beam intensities (X ₁ , X ₂ , X ₃ ...), And on the photoreceptor potential (g (X ₁ ), g (X ₂ ), g ( (X ₃ ),...) Are measured, and (R (X ₁ ), R (X ₂ ), R (X ₃ )...) Satisfying f (X _n ) = g (R (X _n )) are obtained. Then, (X ₁ , R (X ₁ )) and (X ₂ , R (X ₂ )), (X ₂ , R (X ₂ )) and (X ₃ , R (X ₃ )) ... It is customary to use interpolated L (x) instead of R (x). At least x, Xn, g (x), and L (x) are all defined in integers that can be handled by the CPU.

Here, the lookup table L (x) obtained by linear interpolation is for some n that satisfies X _n ≤ x ≤ X _{n + 1} for x
L (x) = int ((xX _n ) (R (X _{n + 1} ) -R (X _n )) / (X _{n + 1} -X _n ) + R (X _n )) 1)
And an expression including multiplication and division. Note that int (x) is a function representing a real number x rounded to the nearest integer in the 0 direction.

  In order to actually find L (x), this equation must be applied repeatedly for the number x of which L (x) is defined. Although the processing power of recent CPUs has been remarkably improved, CPUs mounted on image forming apparatuses often have extremely low processing power for cost reasons. For this reason, there is a problem that an operation that repeatedly applies such multiplication and division has a very heavy processing load. In the conventional apparatus, the low processing capacity of the CPU is covered by reducing the number of times of calculating L (x), but there is also a problem that the follow-up to the change in the photoreceptor characteristics is slow.

Therefore, the lookup table L (x) is calculated as follows. Note that x is _Xn ≦ x ≦ _{Xn + 1} .

First, ΔY _n = R (X _{n + 1} ) -R (X _n ), ΔX _n = X _{n + 1} -X _n , In = int (ΔY _n / ΔX _n ), F _n = ΔY _n -I _n ΔX _n is set (step S1). However, X _n , X _{n + 1} , ΔY _n , ΔX _n , I _n , F _n , x, R (x) are all integers that can be handled by the CPU.

Next, x = _Xn , _Li (x) = R ( _Xn ), and _Lf (x) = 0 are set (step S2).

If x ≧ X _{n + 1} (step S3 / YES), the process ends.

In step S4, if L _f (x) + F _n ≧ + ΔX _n , L _i (x + 1) = L _i (x) + I _n +1, L _f (x + 1) = L _f (x ) + and Fn-ΔX _n. If L _f (x) + F _n ≤ -ΔX _n, then L _i (x + 1) = L _i (x) + I _n -1, L _f (x + 1) = L _f (x) + and Fn + ΔX _n. If -ΔX _n <L _f (x) + F _n <+ ΔX _n, then L _i (x + 1) = L _i (x) + I _n , L _f (x + 1) = L _f (x) + _Let it be F _n .

Replace x with x + 1 (step S4), and return to Step 3. L _i (x) obtained in this way is equal to L (x) in (Equation 1).

  In the conventional method, when the look-up table L (x) for gray value replacement is obtained by linear interpolation, it is necessary to perform multiplication and division by the number of x, which takes much processing time. On the other hand, when the present invention is used, if multiplication and division are performed only once at the beginning, linear interpolation can be performed only by addition and subtraction, and the processing time can be shortened.

  X and L (x) defined in the first embodiment described above are defined in integer regions. Furthermore, since many commercially available image forming apparatuses perform 256 gradation image processing, they are often defined in the range of 0 to 255. On the other hand, when L (x) is obtained by performing linear interpolation from R (x) in (Equation 1), the fractional part is rounded down, and the average is calculated to be 1/2 smaller than when calculated with infinite precision. Will be. This corresponds to about 0.2% of the gray value range, and becomes a non-negligible error when performing more accurate gradation reproduction control.

Therefore, the definition of the lookup table L (x)
L (x) = int ({2 (xX _n ) (R (X _{n + 1} ) -R (X _n )) + (X _{n + 1} -X _n )} / 2 (X _{n + 1} -X _n ) ) + R (X _n ) ... (Formula 2)
Then, since L (x) is obtained by rounding off R (x) by linear interpolation, the average value is the same as that calculated with infinite accuracy, and tone reproducibility is improved. However, if L (x) is calculated according to this definition, the calculation burden increases further than the definition in (Equation 1).

Therefore, if the look-up table L (x) is defined as follows using the variables in the first embodiment, the same result as in (Equation 2) can be obtained without performing complicated calculations. That is, more precise gradation controllability can be achieved without increasing the processing time.
2L _f (x) ≧ + ΔX _n , L (x) = L _i (x) +1
If 2L _f (x) ≤ -ΔX _n, then L (x) = L _i (x) -1
If -ΔX _n <2L _f (x) <+ ΔX _n , h (x) = L _i (x)

In the image forming apparatus, it is important to reflect the gray value of the read image of the original document as accurately as possible in the gray level of the image on the paper, that is, gradation reproducibility. However, since temporal variation factors as exemplified below are involved, the gradation reproduction characteristics that are actually obtained vary with the passage of the month and day, and also due to the environment in which the device is used and individual differences. Go.
Image scanner: individual difference in sensitivity of image sensor, aging change of light quantity of lamp for writing original photosensitive drum: aging change of charging voltage of charger, change of natural discharge amount due to humidity, change of charging characteristics of photoconductor ROS: Change in laser output due to aging / temperature change of laser diode Developer: Change in development characteristics due to changes in humidity, toner type, development bias voltage, etc.Transfer: Change in transfer characteristics due to humidity and paper quality Fuser: Fixing characteristics due to temperature fluctuation change of

In order to maintain the gradation reproducibility by correcting these fluctuation factors, the following gradation reproduction control is performed. (1) The image processing means forms an image of a known specified gray value x and uses it as a patch on the paper. To form. The density of the patch should ideally be the same as the density value generated by the image processing means, but as described above, it often does not match the reality.
(2) The image is read using the image scanner on the paper on which the image including the patch is formed. The image scanner searches the image data for the position where the patch is formed, and reads the gray value g (x) of the patch.
(3) The relationship between x and g (x) is investigated, and a function R (x) = g ⁻¹ (x) that replaces the gray value is created.
(4) This replacement function R (x) is set in the gray value replacement means. During the subsequent image formation, the image processing means replaces the gray value using the gray value replacement means. As a result, the gray value input to the image processing unit is the same as the gray value of the formed image.

  However, the operation of causing the image scanner to read a patch needs to be performed for each gray value, and it is not realistic to form and read a patch with all the gray values that can be used. For this reason, several default gray values are selected, and the linear interpolation as described in Example 1 is performed continuously from the gray value x defined discretely and the gray value g (x) read by the image scanner. The defined L (x) can be obtained and a lookup table can be created from this.

However, with simple linear interpolation, the gray value replacement may be saturated. In other words, there are X ₁ and X ₂ as gray values, and there are cases where L (X ₁ ) = L (X ₂ ) even though the relationship X ₁ <X ₂ is established. If such a look-up table is used, the difference in the gray value existing in the original image cannot be reproduced in the output image. (For the sake of explanation, the case where the gray value replacement is saturated in the high density region is considered below, but it can also be applied to the low density region.)

In order to avoid the above problem, a method of performing interpolation while maintaining the magnitude relationship without saturating the value after replacement is conceivable instead of linear interpolation. For example, there are ₃ pairs of gray value and gray value after replacement, such as P ₀ = (X ₀ , Y ₀ ), P ₁ = (X ₁ , Y ₁ ), P ₂ = (X ₂ , Y ₂ ) (Represented as Y _n = R (X _n )), X ₀ ≦ X ₁ ≦ X ₂ and Y ₀ ≦ Y ₁ ≦ Y ₂ are satisfied. This condition is natural because X _n can be arbitrarily determined and R (x) is usually considered to be a monotonically increasing function. The two-dimensional Bezier interpolation B having the control points P ₀ , P ₁ , and P ₂ is always Y ₀ ≦ B (u) ≦ B (v) ≦ Y with respect to X ₀ ≦ u ≦ v ≦ X ₂ . _{Since 2} is satisfied, it is suitable for avoiding the above problem.

In the following, in addition to the above conditions, it is assumed that [X ₀ , X ₂ ] includes a region that satisfies X ₁ = (X ₀ + X ₂ ) / 2 and in which the substitution is saturated in the gray value region.

Here, the N-dimensional Bezier interpolation B (t) = (x (t), y (t)) is expressed as the following equation (3).

Where B _{n, i} (t) is an nth-order Bernstein polynomial,
B _{n, i} (t) = t ⁱ (1-t) ⁿⁱ n! / (Ni)! I!

Since N = 2, x (t) = (1-t) ² X ₀ + 2t (1-t) X ₁ + t ² X ₂
= (1-t) ² X ₀ + 2t (1-t) (X ₀ + X ₂ ) / 2 + t ² X ₂
= (X ₂ -X ₀ ) t + X ₀
Therefore, t = (x (t) -X ₀ ) / (X ₂ -X ₀ ), 1-t = (X ₂ -x (t)) / (X ₂ -X ₀ ), and t = 0 to X = X _{0 to} X ₂ corresponds to 1

On the other hand, y (t) = (1-t) ² Y ₀ + 2t (1-t) Y ₁ + t ² Y ₂
= {(X ₂ -x (t)) ² Y ₀ +2 (x (t) -X ₀ ) (X ₂ -x (t)) Y ₁ + (x (t) -X ₀ ) ² Y ₂ } / (X ₂ -X ₀ ) 2
If y (t) is represented by x,
y (x) = {(X ₂ -x) ² Y ₀ +2 (xX ₀ ) (X ₂ -x) Y ₁ + (xX ₀ ) ² Y ₂ } / (X ₂ -X ₀ ) ²
= ((Y ₀ -2Y ₁ + Y ₂ ) x ² -2 (X ₂ Y _0- (X ₀ + X ₂ ) Y ₁ + X ₀ Y ₂ ) x + (X ₂ ² Y ₀ -2X ₀ X ₂ Y ₁ + X ₀ ² Y ₂ )} / (X ₂ -X ₀ ) ² (Formula 4)

  In order to calculate the lookup table L (x), (Equation 3) is applied to all possible x, and L (x) = int (y (x)). However, since (Equation 4) includes many multiplications and divisions, there is a problem that a CPU with a low processing capability mounted in the image forming apparatus requires a lot of processing time.

Therefore, in this embodiment, integer constants A, B, C, D are introduced,
A = (Y ₀ -2Y ₁ + Y ₂ ),
B = -2 (X ₂ Y _0- (X ₀ + X ₂ ) Y ₁ + X ₀ Y ₂ ),
C = (X ₂ ² Y ₀ -2X ₀ X ₂ Y ₁ + X ₀ ² Y ₂ ),
D = (X ₂ -X ₀ ) ²
Then, y (x) can be expressed as the following equation (where D> 0, x = X _{0 to} X ₂ ).
y (x) = (Ax ² + Bx + C) / D

The first derivative u (x) and the second derivative v (x) with respect to x of y (x) are defined as follows.
u (x) = dy / dx = y (x + 1) -y (x) = (2Ax + B) / D
v (x) = d ² y / dx ² = u (x + 1) -u (x) = 2A / D
v (x) is a constant that does not depend on x, of which the integer part is represented by V _i and the part after the decimal point is represented by V _f / D. Similarly, u _i (x) is the integer part of u (x), u _f (x) / D is the part after the decimal point, and y _i (x) is the integer part of y (x). Are represented by y _f (x) / D. Then, the Bezier interpolation can be obtained by the following procedure.

Step10 (Initial value setting)
The values corresponding to y (x), u (x), and v (x) at x = X ₀ are obtained as follows.
V _i = div (2A, D)
V _f = 2A-V _i D
u _i (X ₀ ) = div (2AX ₀ + B, D)
u _f (X ₀ ) = (2AX ₀ + B) -u _i (X ₀ ) D
y _i (X ₀ ) = div (AX ₀ ² + BX ₀ + C, D)
y _f (X ₀ ) = (AX ₀ ² + BX ₀ + C) -y _i (X ₀ ) D
Where div (x, y) is div (x, y) = int (x / y) for x ≧ 0 and div (x, y) =-int (-x for x <0 , y), which represents an integer division operation realized by a general CPU.

Step 11 (Find y (x + 1))
Since y (x + 1) = y (x) + u (x), find y (x + 1) as follows
case1: When y _f (x) + u _f (x) ≧ D
y _i (x + 1) = y _i (x) + u _i (x) +1
y _f (x + 1) = y _f (x) + u _f (x) -D
case 2: y _f (x) + u _f (x) ≤ -D
y _i (x + 1) = y _i (x) + u _i (x) -1
y _f (x + 1) = y _f (x) + u _f (x) + D
case 3: -D <y _f (x) + u _f (x) <D
y _i (x + 1) = y _i (x) + u _i (x)
y _f (x + 1) = y _f (x) + u _f (x)
Step12 (Find u (x + 1))
Since u (x + 1) = u (x) + v (x), find u (x + 1) as follows
case1: When u _f (x) + V _f ≧ D
u _i (x + 1) = u _i (x) + V _i +1
u _f (x + 1) = u _f (x) + V _f -D
case2: When u _f (x) + V _f ≤ -D
u _i (x + 1) = u _i (x) + V _i -1
u _f (x + 1) = u _f (x) + V _f + D
case 3: -D <u _f (x) + V _f <D
u _i (x + 1) = u _i (x) + V _i
u _f (x + 1) = u _f (x) + V _f

Step 13: (Proceed x)
Update x with x ← x + 1. to continue the process returns to x <X ₂ if Step11. Y _i (x) obtained in this way is equal to the lookup table L (x) calculated from y (x) defined by (Equation 4).

  In the conventional method, when the look-up table L (x) for gray value replacement is obtained by Bezier interpolation, a complicated expression including multiplication and division must be calculated, which takes a very long processing time. On the other hand, if the present invention is used, if multiplication and division are performed only once, then Bezier interpolation can be performed only by addition and subtraction, and the processing time can be shortened.

  The embodiment described above is a preferred embodiment of the present invention. However, the present invention is not limited to this, and various modifications can be made without departing from the scope of the present invention.

1 is a diagram illustrating a configuration of an image forming apparatus. It is a figure which shows the structure of an image process part. It is a figure which shows the electric constitution of a control system. FIG. 5 is a diagram illustrating a processing procedure according to the first embodiment. FIG. 10 is a diagram illustrating a processing procedure of Example 3.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Original stand 2 Original 3 Color CCD sensor 4 Image processing part 5C, 5M, 5Y, 5K Image forming unit 6C, 6M, 6Y, 6K Photosensitive drum 7C, 7M, 7Y, 7K ROS
8C, 8M, 8Y, 8K Developer 20 Controller 21 CPU 22 RAM
23 ROM 24 I / O section 31 Power supply circuit 32 Potential sensor 33 Toner density sensor 34 Image scanner

Claims (7)

A lookup table,
A laser writing means for referring to the look-up table and controlling the laser beam so as to obtain a laser output corresponding to the gray value of the image;
An image forming apparatus comprising: the rewriting means for rewriting the lookup table by linearly interpolating the discretely defined lookup table by a digital differential analysis method.   2. The image forming apparatus according to claim 1, wherein the rewriting means rounds off the decimal point when linearly interpolating the discretely defined lookup table.   The image forming apparatus according to claim 1, wherein the rewriting unit rewrites the lookup table by performing Bezier interpolation on a discretely defined lookup table. The image forming apparatus includes a photoconductor and a sensor capable of measuring a potential on the photoconductor,
The image forming apparatus according to claim 1, wherein the look-up table is updated based on a potential on the photoconductor. The image forming apparatus has an intermediate transfer member and a sensor capable of measuring the density of the toner transferred onto the intermediate transfer member;
The image forming apparatus according to claim 1, wherein the look-up table is updated based on a toner density transferred onto the intermediate transfer member. The image forming apparatus has a printing mechanism for paper and a sensor capable of measuring the output image density printed on the paper,
4. The image forming apparatus according to claim 1, wherein the look-up table is updated based on a printed output image density. The image forming apparatus according to claim 6, wherein the sensor capable of measuring the output image density is an image scanner capable of reading an image as a document.

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