# Patent

## Title
Image forming apparatus and image forming system

## Abstract

An image forming apparatus comprises an image data generating unit configured to convert a tone of an input value which indicates a density of a pixel by using a predetermined dither matrix and generate image data. The image forming apparatus further comprises a drive source and a gear configured to transmit a drive force from the drive source to an image carrier. The dither matrix includes a plurality of sub-matrixes arranged in a predetermined rule and a dot in each of the plurality of the sub-matrixes grows from a corresponding original point. The image forming apparatus satisfies a relation of (1) a≧0.24 mm and b/a<0.78, or (2) a<0.24 mm and b/a>1.2, where “a” is a travel distance of a printing medium per tooth of the gear in a secondary scanning direction orthogonal to the primary scanning direction, and “b” is a component in the secondary scanning direction of a distance between the original point of the dot derived from a first sub-matrix and the original point of the dot derived from a second sub-matrix.

## Background
CROSS REFERENCE TO RELATED APPLICATION
This application claims priority to and the benefit of Japanese Patent Application No. 2008-223181, filed Sep. 1, 2008, the entire subject matter and disclosure of which is incorporated herein by reference.
BACKGROUND
1. Technical Field
The present invention relates to an image forming apparatus and an image forming system which performs halftoning by using a dither matrix.
2. Description of the Related Art
In a known image forming apparatus of an electrophotographic type, an electrically charged photoconductor drum is irradiated with a light source such as a laser and the voltage of a corresponding portion of the photoconductor drum is changed to cause toner to adhere thereto. Then, a toner image formed on the photoconductor drum is transferred to a printing paper by a transfer roller applied with a voltage opposite from the photoconductor drum. Thereafter, a fixing roller fixes the toner with heat and pressure. Accordingly, a printing result is obtained on the printing paper.
Here, in order to express tones of an image artificially, there is a case such that a halftoning using a dither matrix is performed. By the halftoning, for example, input image data of 256 tones is converted into two-tone output image data, and an image is formed on the basis of the output image data, so that dots of a size according to the tone are arranged discretely at regular pitches, whereby an image in which the tone is artificially reproduced is formed.
However, when the photoconductor drum is driven by a drum gear, a drive force from a drive motor is transmitted to the photoconductor drum via a drive gear and the above-described drum gear engaging therewith. In this configuration, when the drive gear and the drum gear engage, the uneven rotation occurs. It may causes that the pitches of the dots discretely arranged and the cycle of uneven rotation get closer as a result of the halftoning, interference may occur between them, and inconsistencies in density may be generated.
SUMMARY
A need has arisen to provide an image forming apparatus and an image forming system in which generation of inconsistencies in density in a printing medium may be reduced or restrained.
According an embodiment of the present invention, an image forming apparatus comprises an image data generating unit configured to convert a tone of an input value which indicates a density of a pixel by using a predetermined dither matrix and generate image data. The image forming apparatus further comprises a scanning unit configured to scan an image carrier in a primary scanning direction according to the image data generated by the image data generating unit and an image forming unit configured to form, on a printing medium, an image corresponding to the image data scanned by the scanning unit. The image forming apparatus still further comprises a drive source and a gear configured to transmit a drive force from the drive source to the image carrier. The dither matrix includes a plurality of sub-matrixes arranged in a predetermined rule and each of the plurality of sub-matrix having predetermined threshold values such that a dot in each of the plurality of the sub-matrixes grows from a corresponding original point. The plurality of sub-matrixes includes a first sub-matrix and a second sub-matrix which has a predetermined positional relation with the first sub-matrix. The image forming apparatus satisfies a relation of (1) a≧0.24 mm and b/a<0.78, or (2) a<0.24 mm and b/a>1.2, where “a” is a travel distance of a printing medium per tooth of the gear in a secondary scanning direction orthogonal to the primary scanning direction, and “b” is a component in the secondary scanning direction of a distance between the original point of the dot derived from the first sub-matrix and the original point of the dot derived from the second sub-matrix.
According an embodiment of the present invention, an image forming system comprises an image forming apparatus and a computer which communicate with the image forming apparatus. The image forming apparatus comprises a scanning unit configured to scan an image carrier in a primary scanning direction according to image data and an image forming unit configured to form, on a printing medium, an image corresponding to the image data scanned by the scanning unit. The image forming apparatus further comprises a drive source and a gear configured to transmit a drive force from the drive source to the image carrier. The computer comprises an image data generating unit configured to convert an input value which indicates a density of a pixel by using a predetermined dither matrix and generate image data. The dither matrix includes a plurality of sub-matrixes arranged in a predetermined rule and each of the plurality of sub-matrix having predetermined threshold values such that a dot in each of the plurality of the sub-matrixes grows from a corresponding original point. The plurality of sub-matrixes includes a first sub-matrix and a second sub-matrix which has a predetermined positional relation with the first sub-matrix. The image forming system satisfies a relation of (1) a≧0.24 mm and b/a<0.78, or (2) a<0.24 mm and b/a>1.2, where “a” is a travel distance of a printing medium per tooth of the gear in a secondary scanning direction orthogonal to the primary scanning direction, and “b” is a component in the secondary scanning direction of a distance between the original point of the dot derived from the first sub-matrix and the original point of the dot derived from the second sub-matrix.



BRIEF DESCRIPTION OF THE DRAWINGS
For a more complete understanding of the present invention, the needs satisfied thereby, and the features and advantages thereof, reference now is made to the following descriptions taken in connection with the accompanying drawings.
FIG. 1 is a schematic cross-sectional view of a laser printer as an embodiment of an image forming apparatus.
FIG. 2 is a schematic drawing showing a drum driving mechanism.
FIG. 3 is a block diagram showing an electric configuration of the laser printer.
FIG. 4 is a drawing showing an example of a dither matrix.
FIG. 5A is a conceptual drawing showing a relation between original points of dots arranged regularly on a printing paper and ranges that sub-matrixes cover.
FIG. 5B is a drawing showing arrows passing through the original points of the dots formed on the printing paper in parallel to a primary scanning direction being overlapped with the conceptual drawing shown in FIG. 5A.
FIG. 5C is a drawing showing displacement of the positions of formation of the original points of the dots due to the deviation of transport.
FIG. 6A is a drawing showing a relation between a sub-matrix having 3×3 elements and a basic unit formed as an assembly of the sub-matrixes.
FIG. 6B is a conceptual drawing showing a range that a dither matrix in Pattern 1 formed by combining the basic units as shown in FIG. 6A covers.
FIG. 7A is a drawing showing a relation between a sub-matrix having 3×3 elements and a basic unit formed as an assembly of the sub-matrixes.
FIG. 7B is a conceptual drawing showing a range that a dither matrix in Pattern 2 formed by combining the basic units as shown in FIG. 7A covers.
FIG. 8A is a drawing showing a relation between a sub-matrix having 4×4 elements and a basic unit formed as an assembly of the sub-matrixes.
FIG. 8B is a conceptual drawing showing a range that a dither matrix in Pattern 3 formed by combining the basic units as shown in FIG. 8A covers.
FIG. 9A is a drawing showing a relation between a sub-matrix having 4×4 elements and a basic unit formed as an assembly of the sub-matrixes.
FIG. 9B is a conceptual drawing showing a range that a dither matrix in Pattern 4 formed by combining the basic units as shown in FIG. 9A covers.
FIG. 10 is a conceptual drawing showing a dither matrix in Pattern 5 formed by combining the sub-matrixes including 3×3 elements, and a range that the dither matrix covers.
FIG. 11 is a conceptual drawing showing a dither matrix in Pattern 6 formed by combining the sub-matrixes including 4×4 elements, and a range that the dither matrix covers.
FIG. 12A is a conceptual drawing showing a range that a dither matrix in Pattern 7 covers.
FIG. 12B is a conceptual drawing showing a range that a dither matrix in Pattern 8 covers.
FIG. 13 is a drawing showing a result of experiment which has inspected an adequate range of a gear pitch a for respective line pitches b when the dither matrixes from Pattern 1 to Pattern 8 described with reference to FIG. 6 to FIG. 12B are applied.
FIG. 14A is a drawing showing a basic unit configured as an assembly of the sub-matrixes having 4×4 elements.
FIG. 14B is a drawing for explaining a relation between an arrangement of the sub-matrixes, a screen angle, and the number of screen lines.
FIG. 14C is a drawing for explaining the relation between the arrangement of the sub-matrixes, the screen angle, and the number of screen lines.
FIG. 15A is a drawing showing a relation between the arrangement of the sub-matrixes and a screen angle θ.
FIG. 15B is a drawing showing the relation between the arrangement of the sub-matrixes and the screen angle θ.
FIG. 15C is a drawing showing the relation between the arrangement of the sub-matrixes and the screen angle θ.
FIG. 16A is a drawing showing a relation between the basic unit and the dither matrix configured as an assembly of the basic unit.
FIG. 16B is a drawing showing an example of smallest threshold values to be allocated to the respective sub-matrixes.
FIG. 17 is a drawing for explaining a method of determining the size of a large dither.
FIG. 18A is a drawing showing an example of a sequence of growth of the dot for forming a rod-like dot parallel to the primary scanning direction.
FIG. 18B is a drawing showing an example of the threshold values allocated to the dither matrix according to the smallest threshold value shown in FIG. 16B and the sequence of the growth of the dot shown in FIG. 18A.
FIG. 19A is a drawing explaining an example of adjustment of the threshold values arranged in the dither matrix.
FIG. 19B is a drawing explaining an example of the adjustment of the threshold values arranged in the dither matrix.
FIG. 20 is a block diagram showing an electric configuration between a PC and a laser printer connected to the PC so as to allow the communication therewith.



DESCRIPTION OF THE PREFERRED EMBODIMENTS
Embodiments of the present invention and their features and advantages may be understood by referring to FIGS. 1-20, like numerals being used for like corresponding parts in the various drawings.
FIG. 1 is a schematic cross-sectional view of a laser printer 1 as an embodiment of an image forming apparatus. As shown in FIG. 1, the laser printer 1 comprises a printer casing 4 comprising an upper casing 2 and a lower casing 3, a laser scanner apparatus 5 provided on the upper casing 2, a process cartridge 6 demountably provided on the lower casing 3, a transferring and separating device 9 comprising a transfer charger 7 and a charge removing needle 8, a fixing device 12 comprising a heat roller 10 and a pressure roller 11, and a transporting apparatus 17 comprising a paper feeding roller 13, a resist roller 14, a transfer roller 36 configured to transfer a visible image on a photoconductor drum 28 to a printing paper 33, a transporting roller 15, and a paper-discharging roller 16.
The laser scanner apparatus 5 comprises a semiconductor laser 22, a hexahedron mirror 23, an imaging lens 24, a reflecting mirror 25, and a lens member 27 formed of synthetic resin provided at a laser light outlet portion 26. The process cartridge 6 is demountably disposed in the lower casing 3, and comprises the photoconductor drum 28 and a developing cylinder 30 integrally assembled in the interior thereof.
A laser light 35 emitted from the semiconductor laser 22 and entered into the hexahedron mirror 23 is deflected by a predetermined angle via every mirror surfaces of the hexahedron mirror 23 rotating at a constant high speed for primary scanning over a predetermined angular range, is passed through the imaging lens 24, is reflected vertically downward by the reflecting mirror 25, then is passed through the lens member 27 elongated in a scanning direction of the laser light 35, and enters the photoconductor drum 28. The laser light 35 entered into the photoconductor drum 28 performs a secondary scanning with the photoconductor drum 28 rotating at a constant velocity by a drum driving mechanism 40 (shown in FIG. 2) described later, so that an electrostatic latent image is formed on a peripheral surface of the photoconductor drum 28. The laser printer 1 scans the photoconductor drum 28 according to image data described later to form an electrostatic latent image according to the image data.
The electrostatic latent image formed on the photoconductor drum 28 is developed by toner supplied from the developing cylinder 30 and is transferred onto the printing paper 33, then the printing paper 33 is separated from the photoconductor drum 28 by the charge removing needle 8 and is transported to the fixing device 12. The fixing device 12 is configured to fuse and fix the toner to the printing paper 33 by the heat roller 10 and the pressure roller 11, and then transport the printing paper 33 onto a paper discharging tray 34 via the transporting roller 15 and the paper-discharging roller 16.
FIG. 2 is a schematic drawing showing the drum driving mechanism 40. A large-diameter drum gear 41 formed of synthetic resin is secured to a drum shaft 28a of the photoconductor drum 28, and a small-diameter drum driving gear 42 which engages the drum gear 41 is driven to rotate by a coupling mechanism coupled to a main motor M as a drive source. In other words, the drum driving mechanism 40 comprises gears 41, 42 configured to transmit a drive force from the main motor M to the photoconductor drum 28. In contrast, the paper feeding roller 13, the resist roller 14, the transfer roller 36, the transporting roller 15, the paper-discharging roller 16, and the like described with reference to FIG. 1 are configured to be driven to rotate by the main motor M synchronously with the velocity of rotation of the photoconductor drum 28. In other words, the printing paper 33 is configured to be transported synchronously with the rotation of the photoconductor drum 28.
Here, in a case where the drum gear 41, that is, the photoconductor drum 28 is driven to rotate by the rotation of the drum driving gear 42, since it is achieved by engagement between gear teeth 42a of the drum driving gear 42 and gear teeth 41a of the drum gear 41, an engaging operation from a start-of-engagement phase angle to an end-of-engagement phase angle of the gear tooth 42a with respect to the gear tooth 41a is repeated at every tooth 41a of the drum gear 41 and, consequently, the velocity of rotation of the drum gear 41, that is, of the photoconductor drum 28 changes every pitch angle α between the adjacent two gear teeth 41a depending on accuracy of finishing or material of the drum gear 41.
When the drum gear 41 is rotated by the pitch angle α, that is, by a circular pitch (obtained by dividing a pitch circle by the number of teeth) a travel distance by which a point on a surface of the photoconductor drum 28 is moved is defined as a gear pitch “a”. The value of the gear pitch “a” is obtained by a unit of mm. Since the photoconductor drum 28 is subjected to unevenness of the velocity of rotation when the gear tooth 41a engages the gear tooth 42a, inconsistencies in density occur on a printing result on the printing paper 33 every gear pitch a due to the unevenness of the velocity.
FIG. 3 is a block diagram showing an electric configuration of the laser printer 1. As shown in FIG. 3, a video controller 50 of the laser printer 1 comprises a CPU 51, a ROM 52 in which various control programs stored therein, a RAM 53 provided with various memories such as receiving buffers configured to receive and store image data transmitted from a data transmitting instrument (not shown) such as a personal computer or a host computer, a serial interface (S.I/F) 54 configured to receive data transmitted from the external data transmitting instrument (not shown), and a video interface (V.I/F) 55 configured to output print data converted into bit image data in sequence to a DC controller 58, and these members are connected respectively to the CPU 51.
Here, a printing mechanism PM is provided with the above-described laser scanner apparatus 5, the process cartridge 6, the transferring and separating device 9, the fixing device 12, and the transporting apparatus 17, as well as the main motor M which drives the photoconductor drum 28 and the transporting apparatus 17, a fixing heater for the heat roller 10, and other electrical component circuits, and the DC controller 58 is configured to control the drive of a scanner motor which drives the semiconductor laser 22 and the hexahedron mirror 23 in addition to the main motor M, the fixing heater, and various electric component circuits.
The ROM 52 stores a preset dither matrix 52a in addition to the various control programs provided in normal laser printers. The CPU 51 functions as image data generating unit configured to generate image data by performing a halftoning according to the control programs stored in the ROM 52.
In the halftoning, the dither matrix 52a is superimposed on an input image, and input values which represent densities of pixels of the input image are compared with threshold values, which are elements constituting the dither matrix 52a, in one-to-one correspondence. Then, when the input value is equal to or larger than the threshold value, the input value is converted into “1” which means that the toner is fixed to the pixels having the corresponding input value, and if the input value is smaller than the threshold value, the input value is converted into “0” which means that the toner is not fixed to the pixels having the corresponding input value, so that the input values of the 256 tones are converted into two-tone image data. Therefore, the larger the number of pixels having the input values equal to or larger than the threshold value in the pixels within a range that the dither matrix 52a covers, the more the pixels on which the toner is to be fixed within the corresponding range increases, so that the tones of the image can be artificially expressed. Here, the CPU 51 corrects and outputs the image data by a known image processing such as gamma correction or the like together with the halftoning.
FIG. 4 is a drawing showing an example of the dither matrix 52a stored in the ROM 52 of the laser printer 1. In the halftoning, the dither matrix 52a is superimposed on the input image in a positional relationship such that a lateral direction of the dither matrix 52a shown in FIG. 4 corresponds to a primary scanning direction, and a vertical direction of the dither matrix 52a corresponds to a secondary scanning direction, so that the threshold values and the input values of the pixels are compared.
As shown in FIG. 4, the dither matrix 52a includes sets of sixteen sub-matrixes 60 arranged regularly.
In each of the sub-matrixes 60, a smallest threshold value within the sub-matrix 60 (hereinafter, referred simply as smallest threshold value) is arranged at a left end of an uppermost row. Then, in the uppermost row, a row of threshold values arranged in an ascending order from the left end to a right end is allocated. In a second uppermost row, a row of threshold values arranged in the ascending order from a threshold value which is next largest after the rightmost threshold value of the uppermost row is allocated. In this manner, the threshold values are arranged in sequence so as to be larger as it goes toward the lower rows.
In other words, the sub-matrix 60 includes the threshold values set in such a manner that one dot formed at an original point which corresponds to the smallest threshold value extends in the primary scanning direction as the density of the pixel within a range that the sub-matrix 60 covers increases to form a rod-like dot shape, and the rod-like dot is increased in thickness in the secondary scanning direction as the density further increases.
Subsequently, arrangement of the sub-matrixes 60 which constitute the dither matrix 52a will be described. As shown in FIG. 4, in the dither matrix 52a, the sub-matrixes 60 adjacent to each other in the lateral direction (corresponding to the primary scanning direction) are arranged regularly by being shifted by one threshold value in the vertical direction (corresponding to the secondary scanning direction). Since one dot is formed corresponding to one sub-matrix 60 as described above, according to the dither matrix 52a, the respective dots corresponding to the sub-matrixes 60 are formed in regular arrangement so that the original points are shifted in the secondary scanning direction by an extent corresponding to one pixel.
FIG. 5A is a conceptual drawing showing a relation between original points 61 of the dots arranged regularly on the printing paper 33, and ranges 52b that the dither matrixes 52a cover. As described with reference to FIG. 4, sixteen sub-matrixes are included in one dither matrix 52a, and hence sixteen original points 61 at maximum are formed discretely in the range 52b that the one dither matrix 52a covers as shown in FIG. 5A. When the density of the pixel within the range that the dither matrix 52a covers is small, that is, in a low-density portion, the dots each extends from the original point 61 in the primary scanning direction into a rod-like dot shape. In other words, the rod-like dots grow in a direction of arrows shown in FIG. 5B.
There is a case where positions of formation of the dots are shifted in the secondary scanning direction thereby causing uneven dot density due to deviation of transport caused by tolerances of the various components (a displacement caused by variations in the gear pitch a), and hence cyclic inconsistencies in density show up on the printing paper 33. Then, even through such inconsistencies in density are little and inconspicuous, the inconsistencies in density are emphasized due to the interference depending on the relation between the cycle of occurrence of the inconsistencies in density and the distance between the original points 61 described above, so that the image quality might be remarkably lowered. The present inventor focused attention on a relationship among the inconsistencies in density triggered by the deviation of transport caused by the variations in the gear pitch a, the distance between the original points 61 having a positional relationship which is liable to cause the emphasis of the inconsistencies in density, and the gear pitch a.
Referring now to FIG. 5C, the positional relationship which is liable to trigger the inconsistencies in density caused by the deviation of transport will be described. FIG. 5C is a drawing showing displacement of the positions of formation of the original points of the dots due to the deviation of transport.
Assuming that there is no deviation of transport of the printing paper 33, the original point of the dot which is to be formed at a position P2 shown in FIG. 5C is actually formed at a position P2′ shifted by an amount σ in the secondary scanning direction by being influenced by the deviation of transport. The sign σ represents the deviation of transport, that is, an estimated amount of displacement caused by the variations in the gear pitch a. The value of σ can be estimated from the tolerances of the respective components.
When a distance A between a P1 and the P2 is changed to a distance B between the P1 and P2′ due to the deviation of transport, the amount of change causes a change in density per unit area, so that the inconsistencies in density are brought into visual perception.
The present inventor has found that the density change is calculated in the following manner in order to verify an extent of the change in density generated among the dots. First of all, an estimated value of the distance A between the P1 and P2 is calculated using the following expression (1). In the expression, a component in the primary scanning direction of the distance A is expressed by X, and a component in the secondary scanning direction is expressed by Y.

A=√{square root over (X2+Y2)}  (1)

Subsequently, an estimated value of the distance B between the P1 and P2′ is calculated using the following expression (2).

B=√{square root over (X2+(Y+σ)2)}  (2)

The ratio of the change of the distances A and B between the two points is visually perceptible as the inconsistencies in density. Therefore, the density change is defined as the expression (3).




  
    
      
        
          density
          ⁢
          
            
          
          ⁢
          change
        
        =
        
          
            B
            /
            A
          
          =
          
            
              1
              +
              
                
                  
                    σ
                    2
                  
                  +
                  
                    2
                    ⁢
                    y
                    ⁢
                    
                      
                    
                    ⁢
                    σ
                  
                
                
                  
                    X
                    2
                  
                  +
                  
                    Y
                    2
                  
                
              
            
          
        
      
    
    
      
        (
        3
        )
      
    
  




In other words, it is understood that the smaller the distance between the two points and the larger the value of Y (the component in the secondary scanning direction of the distance between the two points), the larger the density change becomes and the higher the probability of occurrence of the inconsistencies in density becomes. The present inventor focused attention on the positional relationship of the original points of the dots which maximize the density change.
More specifically, a first sub-matrix and a second sub-matrix which has a predetermined positional relationship determined on the basis of the above described density change are determined from the plurality of sub-matrixes 60 (see FIG. 4) which constitute the dither matrix 52a. In other words, the first sub-matrix and the second sub-matrix are determined so that the density change between the original point 61 of the dot derived from the first sub-matrix and the original point 61 of the dot derived from the second sub-matrix is maximized. Then, the component in the secondary scanning direction of a distance between the original point 61 of the dot derived from the first sub-matrix and the original point 61 of the dot derived from the second sub-matrix is expressed as a line pitch b (see FIG. 5B), and the laser printer 1 in this embodiment is configured in such a manner that a relationship between the line pitch b and the gear pitch a satisfies a relational expression a≧0.24 mm and b/a<0.78 or a<0.24 mm and b/a>1.2. In this manner, the occurrence of the inconsistencies in density can be restrained adequately. The value of the line pitch b is obtained in a unit of mm.
By determining the first sub-matrix and the second sub-matrix using the density change described above, the component in the secondary scanning direction of the distance between the dots having the relationship which is liable to cause the inconsistencies in density, that is, the relationship such that the distance between the original points of the dots is small and the component in the secondary scanning direction of the corresponding distance is large can be set to be the line pitch b, so that the inconsistencies in density can be reduced or restrained adequately.
Also, in a case of employing a dither matrix having a configuration different from the dither matrix 52a described with reference to FIG. 4 and FIGS. 5A and 5B, the effect of restraining the interference fringes is also achieved by applying the numerical value range described above.
Referring now to FIGS. 6A and 6B to FIG. 13, various dither matrixes having configurations different from the dither matrix 52a are exemplified, and the effect obtained when the numerical value range described above is applied about the various dither matrixes shown in FIGS. 6A and 6B to FIG. 13 will be described.
FIG. 6A is a drawing showing a relation between a sub-matrix 64 having 3×3 elements and a basic unit 66 formed by assembling four sub-matrixes 64. As shown in FIG. 6A, by configuring the basic unit 66 by shifting the sub-matrixes 64 having 3×3 elements by an extent corresponding to three elements in the primary scanning direction and by an extent corresponding to one element in the secondary scanning direction, an angle of a line connecting the original points of the dots formed with respect to the primary scanning direction (hereinafter, referred to as a screen angle θ) becomes about 18°.
A threshold value which does not belong to any sub-matrix 64, which is surrounded by the sub-matrixes 64, is referred to as an inter-sub-matrix cell C, hereinafter. As shown in FIG. 6A, the basic unit 66 is configured to include one inter-sub-matrix cell C.
FIG. 6B is a conceptual drawing showing a dither matrix formed by combining the basic units 66 as shown in FIG. 6A (hereinafter referred to as Pattern 1), and a range that the dither matrix covers. When performing the halftoning using the dither matrix in Pattern 1 at a resolution of 600 dpi, the number of screen lines is about 190 lpi (line per inch), and the line pitch b has a length corresponding to four pixels (about 0.169 mm). The term “the number of screen lines” means a value which indicates the number of original points of the dots included per inch in a direction vertical to a line L connecting the original points of the dots.
FIG. 7A is a drawing showing a relation between the sub-matrix 64 having 3×3 elements and a basic unit 68 formed by assembling four sub-matrixes 64. As shown in FIG. 7A, with the basic unit 68 formed by shifting the sub-matrixes 64 having 3×3 elements by an extent corresponding to one element in the primary scanning direction and by an extent corresponding to three elements in the secondary scanning direction, the screen angle θ becomes about 72°. As shown in FIG. 7A, the basic unit 68 is configured to include one inter-sub-matrix cell C.
FIG. 7B is a conceptual drawing showing a range that a dither matrix formed by combining the basic units 68 as shown in FIG. 7A (hereinafter referred to as Pattern 2) covers. When performing the halftoning using the dither matrix in Pattern 2 at the resolution of 600 dpi, the number of screen lines is about 190 lpi, and the line pitch b has the length corresponding to three pixels (about 0.127 mm).
FIG. 8A is a drawing showing a relation between the sub-matrix 60 having 4×4 elements and a basic unit 70 formed by assembling four sub-matrixes 60. As shown in FIG. 8A, with the basic unit 70 formed by shifting the sub-matrix 60 having 4×4 elements by an extent corresponding to four elements in the primary scanning direction and by an extent corresponding to one element in the secondary scanning direction, the screen angle θ becomes about 14°. As shown in FIG. 8A, the basic unit 70 is configured to include one inter-sub-matrix cell C.
FIG. 8B is a conceptual drawing showing a range that a dither matrix formed by combining the basic units 70 as shown in FIG. 8A (hereinafter referred to as Pattern 3) covers. When performing the halftoning using the dither matrix in Pattern 3 at the resolution of 600 dpi, the number of screen lines is about 145 lpi, and the line pitch b has the length corresponding to five pixels (about 0.212 mm).
FIG. 9A is a drawing showing a relation between the sub-matrix 60 having 4×4 elements and a basic unit 72 formed as an assembly of the sub-matrixes 60. As shown in FIG. 9, with the basic unit 72 formed by shifting the sub-matrix 60 having 4×4 elements by an extent corresponding to one element in the primary scanning direction and by an extent corresponding to four elements in the secondary scanning direction, an angle of the line connecting the original points of dots formed with respect to the primary scanning direction becomes about 76°. The basic unit 72 is configured to include the inter-sub-matrix cell C including two threshold values in total; two in the vertical direction, and one in the lateral direction.
FIG. 9B is a conceptual drawing showing a range that a dither matrix formed by combining the basic units 72 as shown in FIG. 9A (hereinafter referred to as Pattern 4) covers. When performing the halftoning using the dither matrix in Pattern 4 at the resolution of 600 dpi, the number of screen lines is about 137 lpi, and the line pitch b has a length corresponding to four pixels (about 0.169 mm).
FIG. 10 is a conceptual drawing showing a dither matrix in Pattern 5 formed by combining the sub-matrixes 64 including 3×3 elements, and a range that the dither matrix covers. The sub-matrixes 64 shown in FIG. 10 are arranged with the intermediary of the inter-sub-matrix cell C including two threshold values in total; two in the lateral direction and one in the vertical direction, between the four sub-matrixes 64. When performing halftoning using the dither matrix in Pattern 5 at the resolution of 600 dpi, the number of screen lines is about 172 lpi, and the line pitch b has the length corresponding to four pixels (about 0.169 mm). The screen angle is about 18.4°.
FIG. 11 is a conceptual drawing showing a dither matrix in Pattern 6 formed by combining the sub-matrixes 60 including 4×4 elements, and a range that the dither matrix covers. The sub-matrixes 60 shown in FIG. 11 are arranged with the intermediary of the inter-sub-matrix cell C including two threshold values in total; two in the lateral direction and one in vertical direction, between the four sub-matrixes 60. According to the dither matrix in Pattern 6 as described above, the number of screen lines is about 137 lpi, and the line pitch b has the length corresponding to five pixels (about 0.212 mm). The screen angle is about 14°.
FIG. 12A is a conceptual drawing showing a dither matrix in Pattern 7 formed by combining the sub-matrixes 60 including 3×3 elements, and a range that the dither matrix covers. The sub-matrixes 60 shown in FIG. 12A are arranged with the intermediary of the inter-sub-matrix cell C including nine threshold values in total; three in the lateral direction and three in vertical direction, between the four sub-matrixes 60. According to the dither matrix in Pattern 7 as described above, the number of screen lines is about 141 lpi, and the line pitch b has the length corresponding to six pixels (about 0.254 mm). The screen angle is about 45°.
FIG. 12B is a conceptual drawing showing a dither matrix in Pattern 8 formed by combining the sub-matrixes 65 including 5×5 elements, and a range that the dither matrix covers. The sub-matrixes 65 shown in FIG. 12B are arranged with the intermediary of the inter-sub-matrix cell C including one threshold value between the four sub-matrixes 60. According to the dither matrix in Pattern 8 as described above, the number of screen lines is about 118 lpi, and the line pitch b has the length corresponding to six pixels (about 0.254 mm). The screen angle is about 11°.
FIG. 13 is a drawing showing a result of experiment which has inspected an adequate range of the gear pitch a for respective line pitches b when the dither matrixes from Pattern 1 to Pattern 8 described with reference to FIGS. 6A and 6B to FIG. 12 are applied.
The present inventor has done an experiment about whether the inconsistencies in density were generated or not as a result of printing out the image data applied with the halftoning using the dither matrixes from Pattern 1 to Pattern 8 using a laser printer at the resolution of 600 dpi. The number of teeth was changed by changing the outer diameter of the gear while fixing the module of the gear and the gear pitch a was changed accordingly.
In a table shown in FIG. 13, “GOOD” indicates that no inconsistency in density is generated or the inconsistencies in density are restrained to an allowable level, and “NG” indicates that the inconsistencies in density are generated to an extent exceeding the allowable level. Numerical values (b/a) obtained by dividing the line pitch b by the gear pitch a are shown above “GOOD” or “NG” indicate the results of evaluation.
As shown in FIG. 13, a result such that when the relational expression; a≧0.24 mm and b/a<0.78 is satisfied, no inconsistency in density is generated or the inconsistencies in density are restrained to the allowable level was obtained. Also, a result such that when the relational expression; a<0.24 mm and b/a>1.2 is satisfied, no inconsistency in density is generated or the inconsistencies in density are restrained to the allowable level was obtained.
Subsequently, referring now to FIGS. 14A, 14B and 14C to FIGS. 19A, and 19B, a sequence of designing the dither matrix will be described. When designing the dither matrix, first of all, the size (the number of elements) of the sub-matrixes is determined from the intended number of screen lines. For example, when a range of the number of screen lines from 150 lpi to 200 lpi is intended, a size of the sub-matrix of 3×3 is determined. Also, For example, when a range of the number of screen lines from 120 lpi to 150 lpi is intended, a size of the sub-matrix of 4×4 is determined.
Subsequently, arrangement of the sub-matrixes which constitute the basic unit is determined from the intended screen angle and the number of screen lines.
FIG. 14A is a drawing showing a basic unit 62 including four sub-matrixes 60 each having 4×4 elements. With the arrangement of sub-matrixes 60 as shown in FIG. 14A, the screen angle θ of about 14°, and the number of screen lines of about 145 lpi are achieved.
As a matter of course, the screen angle θ and the number of screen lines can be changed as needed by configuring the basic unit by differentiating the size or the arrangement of the sub-matrixes.
FIG. 14B shows an example in which the inter-sub-matrix cell C which corresponds to one element in the vertical direction is interposed between the sub-matrixes 64 of 3×3. In this case, the screen angle θ always becomes about 18°. Also, by increasing and decreasing the number of elements in the inter-sub-matrix cell C in the lateral direction, the number of screen lines can be changed as needed.
In the same manner, FIG. 14C shows an example in which the inter-sub-matrix cell C which corresponds to one element in the lateral direction is interposed between a pair of the sub-matrixes 64 of 3×3. In this case, the screen angle θ always becomes about 72°. Also, by increasing and decreasing the number of elements in the inter-sub-matrix cell C in the vertical direction, the number of screen lines can be changed as needed.
Referring now to FIGS. 15A, 15B and 15C, the relation between the arrangement of the sub-matrixes and the screen angle θ will further be described. FIG. 15A is a drawing showing an example of arrangement of the sub-matrixes for forming a screen angle of about 34°. As shown in FIG. 15A, by arranging the inter-sub-matrix cell C which corresponds to two elements in the vertical direction and one element in the lateral direction so as to be interposed between the sub-matrixes 64 of 3×3, the screen angle of about 34° is achieved.
FIG. 15B is a drawing explaining an example of arrangement of the sub-matrixes for forming a screen angle θ of 45°. As shown in FIG. 15B, by arranging the sub-matrixes 64 of 3×3 so as to be shifted by three elements in the lateral direction and three elements in the vertical direction, the basic unit for forming the screen angle of 45° is configured. By arranging the sub-matrixes of n×n by shifting in the lateral direction and the vertical direction by n elements respectively, the screen angle θ of 45° is achieved in the same manner.
FIG. 15C shows an example in which the inter-sub-matrix cell C which corresponds to two elements in the vertical direction is interposed between the sub-matrixes 60 of 4×4. With the arrangement of the sub-matrixes 60 as shown in FIG. 15C, the screen angle θ of about 27° is achieved.
As described with reference to FIGS. 14A, 14B and 14C and FIGS. 15A, 15B and 15C, by adjusting the size and arrangement of the sub-matrixes, adjustment of the screen angle θ and the number of screen lines to desired values is achieved.
FIG. 16A is a drawing showing a relationship between the basic units 62 and the dither matrix 52a configured as an assembly of the basic units 62. Here, the number of elements in the dither matrix 52a is equal to the number of tones which is expressible within the range that the dither matrix 52a covers. Therefore, the number of the basic units 62 which constitute the dither matrix 52a is calculated on the basis of the desired number of tones which are to be expressed by the dither matrix 52a and the number of elements in the basic unit 62. For example, when the number of tones to be expressed in the dither matrix 52a is 256 tones, and the number of elements in the single basic unit 62 is sixty five, it is understood that the single dither matrix 52a can be configured by four basic units 62 (that is, sixteen sub-matrixes 60).
Subsequently, values from 1 to 16 are allocated as the smallest threshold values to the respective sub-matrixes 60. FIG. 16B is a drawing showing an example of the smallest threshold values to be allocated to the respective sub-matrixes 60. The smallest threshold values allocated here are provisional smallest threshold values allocated temporarily in order to allocate the threshold values of 256 tones to the dither matrix 52a uniformly.
Subsequently, as shown in FIG. 17, the size of a large dither 63 configured of an assembly of the dither matrixes 52a is determined. More specifically, spots where the same smallest threshold values are generated at the same position in the lateral direction and at the same position in the vertical direction are searched, and a size covering a range to the corresponding spots is determined as the size of the large dither 63. For example, as shown in FIG. 16, a spot X1 where the smallest threshold value “1” is generated is determined as an apex, and a size defined by a spot X3 which is located at the same position in the vertical direction as the spot X1 and where the same smallest threshold value “1” is generated and a spot X5 which is located at the same position in the lateral direction as the spot X1 and where the same smallest threshold value “1” is generated is determined as the size of the large dither 63.
A procedure to calculate the distance from the spot X1 to the spot X3 and the distance from the spot X1 to the spot X5 (that is, the size of the large dither 63) will be described below. First of all, a spot X2 where the same smallest threshold value “1” as the spot X1 is generated is searched. In the example shown in FIGS. 15A and 15B, the distance between the spot X1 and the spot X2 is apart from each other by an extent corresponding to sixteen threshold values in the vertical direction and is apart from each other by an extent corresponding to four threshold values in the lateral direction. Also, a range from the spot X2 to a spot X4 where the same smallest threshold value “1” is generated corresponds to sixteen threshold values in the lateral direction and to four threshold values in the vertical direction.
Therefore, from an expression 16÷4=4, it is understood that four dither matrixes 52a can be arranged in a range from the spot X3 to the spot X2. Therefore, the number of threshold values to be arranged in the lateral direction from the spot X2 to the spot X3 is calculated as sixty four from an expression 16×4=64.
The spot X1 and the spot X2 are apart from each other in the lateral direction by an extent corresponding to four threshold values. Therefore, from an expression 64+4=68, the number of the threshold values included in a range from the spot X1 to the spot X3 (that is, the lateral size of the large dither 63) can be calculated as sixty eight threshold values. In the same manner, the number of the threshold values included in a range from the spot X1 to the spot X5 (that is, the vertical size of the large dither) can be calculated.
The dither matrixes designed by the process described later are stored in the ROM 52 (see FIG. 3) in the unit of the large dither determined in this manner.
Subsequently, the shape of the dots to be formed corresponding to the respective sub-matrixes 60 is selected. As the dot shape, there are “circle”, “oval”, “square”, and “diamond shape” in detail, and the dot shape which meets the application or the resolution may be selected. Here, description will be made assuming that the rod-like dot shape which is suitable for the laser printer 1 is selected.
FIG. 18A is a drawing showing an example of a sequence of growth of the dot for forming the rod-like dot parallel to the primary scanning direction. As shown in FIG. 18A, the sub-matrixes 60 and the inter-sub-matrix cell C which assume the desired dot shape can be designed by designing the sub-matrixes 60 and the inter-sub-matrix cell C in such a manner that the larger the sequence of growth of the dot, the larger the threshold value to be allocated becomes, that is, by allocating the threshold values in an ascending order according to the sequence of growth of the dot.
As shown in FIG. 18A, when determining the sequence of growth of the dot, the dot formed corresponding to the sub-matrix 60 is formed into the rod-like dot shape by extending from a position corresponding to the upper left corner of the sub-matrix 60 as an original point in the primary scanning direction.
FIG. 18B is a drawing showing an example of the threshold values allocated to the dither matrix 52a according to the smallest threshold value shown in FIG. 16B and the sequence of growth of the dot shown in FIG. 18A. The smallest threshold value allocated as shown in FIG. 16B is arranged at the upper left corner of the sub-matrix 60, and the threshold values are arranged by adding the smallest threshold value by “16” in the sequence of growth of the dot shown in FIG. 18A (see FIG. 18B). Accordingly, the threshold values from 1 to 256 can be allocated dispersedly. Subsequently, the threshold values arranged in the dither matrix 52a in this manner are fine-adjusted.
FIGS. 19A and 19B are drawings explaining examples of adjustment of the threshold values arranged in the dither matrix 52a. For example, when a feature such that the toner can hardly be fixed is observed in the laser printer 1, the pixels to be adhered with the toner can be increased by reducing the threshold values to be arranged in the dither matrix 52a, so that the dots having an adequate size can be formed even when the toner can hardly be fixed.
Therefore, as shown in FIG. 19A, the provisional smallest threshold values “1, 2, 3, 4” allocated initially to the sub-matrixes are changed to “1” (sub-matrix 60A). In the same manner, the provisional smallest threshold values “5, 6, 7, 8” allocated initially to the sub-matrixes are changed to “2” (sub-matrix 60B). In the same manner, the provisional smallest threshold values “9, 10, 11, 12, 13, 14, 15, 16” allocated initially to the sub-matrixes are changed to “3” (sub-matrix 60C). Subsequently, the threshold values from “4” to “19” as the second smallest threshold values from the smallest threshold values “1, 2, 3” after the change are allocated to immediate right of the smallest threshold value respectively in any sub-matrix. Then, with reference to the allocated threshold values from “4” to “19”, the remaining threshold values in the respective sub-matrixes 60 are set to values with the increment of 16, so that the threshold values in the sub-matrix 60 are reset.
As shown in FIG. 19A, when the threshold values in the respective sub-matrixes 60 are changed, a largest value of the threshold value in the dither matrix 52a is smaller than 255. For example, in the case of FIG. 19A, the largest threshold value is 243. In this case, the values of all the pixels within the range that the dither matrix covers are converted into “1” which means that the toner is fixed at the time point of the input value 243, so that the tone from the input value 243 to the input value 255 cannot be expressed.
Therefore, as shown in FIG. 19B, the threshold values are adjusted so that the largest value among all the threshold values in the dither matrix 52a becomes 255. More specifically, the calculation of “threshold value×255÷(the largest threshold value at the time point of FIG. 19A)”, if for example, the largest threshold value at the time point of FIG. 19A is 243, the calculation of the “threshold value×255÷243” is performed for all the threshold values so that the threshold values to 255 are allocated evenly. Values after the decimal point of the result of calculation are rounded off.
In this manner, as a result of adjustment of the largest value of the threshold values, for example, if any threshold value becomes zero, or an irregularity such that the threshold value next to the threshold value 20 becomes 27 is generated, so that inconvenience such that a smooth tone expression cannot be achieved is resulted, an operator who is in charge of creating the dither matrix 52a may return to any part of the procedure shown in FIGS. 14A, 14B, and 14C to FIGS. 19A and 19B and retry the operation again.
The created dither matrix 52a is stored in the ROM 52 (see FIG. 3) in the unit of the large dither 63 determined in FIG. 17. Accordingly, in the halftoning, a range corresponding to a plurality of the dither matrixes 52a can be processed at once by superimposing the large dither 63 on the input image and performing the comparison with the threshold values.
The dither matrixes from Pattern 1 to Pattern 8 described with reference to FIGS. 6A and 6B to FIG. 12 can be designed in the same procedure.
In this embodiment, description has been made assuming that the laser printer 1 stores the dither matrixes 52a, and the halftoning is performed in the laser printer 1. In contrast, it is also possible to configure in such a manner that the halftoning is performed in the external data processing instrument such as the personal computer and the image data is outputted into the laser printer.
FIG. 20 is a block diagram showing an electric configuration of a personal computer 80 (hereinafter referred to as PC 80), and a laser printer 90 connected to the PC 80 so as to allow the communication therewith. The laser printer 90 comprises a photoconductor drum, a laser scanner apparatus configured to scan the photoconductor drum in the primary scanning direction according to the image data, a drum gear configured to transmit a drive force from the drive source to the photoconductor drum, and a drum driving gear. The configurations of the photoconductor drum, the laser scanner apparatus, the drum gear, and the drum driving gear may be the same configuration as those of the laser printer 1 described in the embodiment, detailed illustration and description are omitted.
The PC 80 comprises a CPU 81, a ROM 82, a RAM 83, an HDD (hard disk drive) 84, and an interface 86 for connecting with the laser printer 90.
As shown in FIG. 20, the HDD 84 stores a printer driver 84a and a dither matrix 84b used for the halftoning. The CPU 81 functions as image data generating unit configured to generate image data by performing the halftoning using the dither matrix 84b according to the printer driver 84a. 
The dither matrix 84b is configured to include a plurality of the sub-matrixes having the threshold values set in such a manner that the dot grows into the rod-like shape from the original point in the primary scanning direction as in the case of the dither matrix 52a in the embodiment arranged regularly.
In this case as well, the generation of the inconsistencies in density on the printing paper is restrained by configuring in such a manner that the gear pitch a determined on the basis of the configuration of the laser printer 90 and the line pitch b determined on the basis of the dither matrix stored in the PC 80 satisfy the relational expression; a≧0.24 mm and b/a<0.78, or a<0.24 mm and b/a>1.2, in the same manner as the laser printer 1 in the embodiment.
Although the number of colors used in the laser printer 1 is assumed to be one in the description in the embodiment described above, a color laser printer which forms images with toner in a plurality of colors may be applicable. When the image is formed with the toner in the plurality of colors, the dither matrixes to be applied are differentiated on the color-to-color basis, and the screen angles are differentiated on the color-to-color basis. In this case as well, the generation of the inconsistencies in density on the printing paper may be reduced or restrained by configuring in such a manner that the line pitch b and the gear pitch a determined from the dither matrixes in respective colors respectively satisfy the relational expression; a≧0.24 mm and b/a<0.78, or a<0.24 mm and b/a>1.2, in the same manner as the laser printer 1 in the embodiment.
While the invention has been described in connection with embodiments, it will be understood by those skilled in the art that other variations and modifications of the embodiments described above may be made without departing from the scope of the invention. Other embodiments will be apparent to those skilled in the art from a consideration of the specification or practice of the invention disclosed herein. It is intended that the specification and the described examples are considered merely as exemplary of the invention, with the true scope of the invention being indicated by the flowing claims.

## Claims

1. An image forming apparatus comprising:
an image data generating unit configured to convert a tone of an input value which indicates a density of a pixel by using a predetermined dither matrix and to generate image data;
a scanning unit configured to scan an image carrier in a primary scanning direction according to the image data generated by the image data generating unit;
an image forming unit configured to form, on a printing medium, an image corresponding to the image data scanned by the scanning unit;
a drive source; and
a gear configured to transmit a drive force from the drive source to the image carrier,
wherein the dither matrix comprises a plurality of sub-matrixes arranged in a predetermined rule and each of the plurality of sub-matrixes having predetermined threshold values, such that a dot in each of the plurality of the sub-matrixes grows from a corresponding original point, the plurality of sub-matrixes comprises a first sub-matrix and a second sub-matrix that has a predetermined positional relation with the first sub-matrix,
wherein the image forming apparatus satisfies a relation of:
(1) a≧0.24 mm and b/a<0.78, or
(2) a<0.24 mm and b/a>1.2,

where “a” is a travel distance of a printing medium per tooth of the gear in a secondary scanning direction orthogonal to the primary scanning direction, and
“b” is a component in the secondary scanning direction of a distance between the original point of the dot derived from the first sub-matrix and the original point of the dot derived from the second sub-matrix, and
wherein the second sub-matrix is one of the sub-matrixes next to the first sub-matrix and is positioned, such that the distance b is greater than the distance b of the other sub-matrixes next to the first sub-matrix.

2. The image forming apparatus according to claim 1, wherein the image forming apparatus satisfies the relation of (1) a≧0.24 mm and b/a<0.78.

3. The image forming apparatus according to claim 1, wherein the image forming apparatus satisfies the relation of (2) a<0.24 mm and b/a>1.2.

4. An image forming system comprising:
an image forming apparatus comprising:
a scanning unit configured to scan an image carrier in a primary scanning direction according to image data;
an image forming unit configured to form, on a printing medium, an image corresponding to the image data scanned by the scanning unit;
a drive source; and
a gear configured to transmit a drive force from the drive source to the image carrier; and

a computer which communicates with the image forming apparatus, the computer comprising an image data generating unit configured to convert an input value which indicates a density of a pixel by using a predetermined dither matrix and to generate image data,
wherein the dither matrix comprises a plurality of sub-matrixes arranged in a predetermined rule, each of the plurality of sub-matrixes having predetermined threshold values, such that a dot in each of the plurality of the sub-matrixes grows from a corresponding original point, the plurality of sub-matrixes comprising a first sub-matrix and a second sub-matrix that has a predetermined positional relation with the first sub-matrix,
wherein the image forming apparatus satisfies a relation of:
(1) a≧0.24 mm and b/a<0.78, or
(2) a<0.24 mm and b/a>1.2,

where “a” is a travel distance of a printing medium per tooth of the gear in a secondary scanning direction orthogonal to the primary scanning direction, and
“b” is a component in the secondary scanning direction of a distance between the original point of the dot derived from the first sub-matrix and the original point of the dot derived from the second sub-matrix, and
wherein the second sub-matrix is one of the sub-matrixes next to the first sub-matrix and is positioned such that the distance b is greater than the distance b of the other sub-matrixes next to the first sub-matrix.

5. The image forming system according to claim 4, wherein the image forming system satisfies the relation of (1) a≧0.24 mm and b/a<0.78.

6. The image forming system according to claim 4, wherein the image forming system satisfies the relation of (2) a<0.24 mm and b/a>1.2.