Abstract:
An apparatus to control color registration and image density using a single mark and method using the same. The image forming apparatus has an image carrying member for carrying thereon an image having a plurality of colors. The image carrying member is configured to move in a first direction substantially perpendicular to a second direction, and a plurality of color marks having different densities are placed on the image carrying member for controlling respective registrations and toner densities of the color marks. One of said color marks includes a polygon having a first side which is not parallel to said first and second directions.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS  
       [0001]     This application is a continuation in part of U.S. Ser. No. 10/232,314, filed Sep. 3, 2002, now pending, which claims the benefit of Korean Patent Application No. 2001-54151 filed Sep. 4, 2001, the disclosures of which are incorporated herein by reference. 
     
    
     BACKGROUND OF THE INVENTION  
       [0002]     1. Field of the Invention  
         [0003]     The present invention relates to an apparatus to control color registration and image density in a printer, and a method of calculating color registration error and image density, and more particularly, to an apparatus to detect both color registration and image density using a single mark and a method using same.  
         [0004]     2. Description of the Related Art  
         [0005]     Image forming apparatuses such as printers and copy machines form a latent electrostatic image by charging a photoconductive member on a transfer belt and performing selective exposure by scanning a laser beam, develop the latent electrostatic image using colored toners and a developer unit, and transfer the developed latent electrostatic image to a recording medium by pressing and heating, thereby forming an image.  
         [0006]     Generally, the colors of toners used in a developer unit are cyan (C), magenta (M), yellow (Y), and black (K). The four color toners are transferred such that the four colors overlap to form a complete image. To deliver high quality images, unit images of individual colors should be accurately superimposed. This superimposition of colors is referred to as color registration.  
         [0007]     Color registration errors can arise from complex causes such as mismatch of the individual color units of the developer unit, errors in processing an optical lens, and motion errors of the transfer belt. Particularly, color registration error becomes a problem in an image forming apparatus having a serial (or tandem) structure including a plurality of developer units.  
         [0008]     Color registration errors may have various causes in a laser scanning unit (LSU) and a belt drive mechanism, and during belt steering and the assembly process. A belt steering error arises from belt weaving or deformation of the belt unit. An error during the assembly process may arise during the assembly of photosensitive drums such as an OPC drum, and the assembly of the LSUs.  
         [0009]     An error in the LSU arises from irregular laser scan speed, asynchronization of a polygon mirror (not shown), jitter in an LSU motor (not shown), nonparallel laser beams, and mismatch in bow between laser beams. Here, asynchronization of a polygon mirror may be caused by inaccurate manufacture or imbalance during horizontal rotation, and causes an error in a scanning line. When laser beams are not parallel due to misalignment or mismatch in laser beam bow, toners are developed in the form of a bow, so an error may occur.  
         [0010]     An error which may occur in a belt and photosensitive drum drive mechanism arises from a change in the diameter of a roll due to temperature, a change in the linear velocity of the transfer belt due to load on the belt, a change in rotary speed due to load on the photosensitive drum, and irregular driving of a transfer belt drive roller.  
         [0011]     Color registration errors have four types: X-offset, Y-offset, printing width error, and skew. X-offset arises in a scan direction in which an LSU scans its laser light onto a photoconductive member. Y-offset arises in a cross-scan direction in which the transfer belt moves. Printing width errors arise from a difference in width of an image area. Skew arises from displacement of a development line. In order to obtain high quality images using color registration, a sensor to detect color registration errors and a method of accurately calculating the errors are required.  
         [0012]      FIG. 1  is a diagram of a color registration sensor and a mark pattern disclosed in U.S. Pat. No. 5,287,162. Referring to  FIG. 1 , a color registration mark pattern  13  in a chevrog shape is formed on a transfer belt (not shown). A split sensor  11  including two split cells  11   a  and  11   b  detects a beam reflected from the color registration mark pattern  13 . A cross scan direction and a scan direction are also illustrated. Colors of the marks (y, m, k) are also illustrated.  
         [0013]     In addition to color registration, i.e., arrangement of colors in juxtaposition, it is also necessary to appropriately adjust image density in order to obtain high quality images. However, a disadvantage of the mark pattern of  FIG. 1  is that image density cannot be detected. Conventional apparatuses may radiate beams on a different type of mark to determine image density. For example, a rectangular mark with sides extending in the scan and sub-scan directions may be used, as shown in  FIG. 2 . However, this image density mark cannot be used to detect color registration errors. Thus, separate marks and possibly separate sensors must be provided for each of the color registration error and image density detection. This results in additional parts and additional time required to perform the detecting operations.  
       SUMMARY OF THE INVENTION  
       [0014]     Accordingly, it is an aspect of the present invention to provide a color registration and image density control apparatus capable of detecting color registration errors and image density using a same mark.  
         [0015]     The foregoing and/or additional aspects and/or advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.  
         [0016]     The foregoing and/or other aspects of the invention are achieved by providing in an image forming apparatus having an image carrying member for carrying thereon an image having a plurality of colors, said image carrying member being configured to move in a first direction substantially perpendicular to a second direction, a plurality of color marks having different densities being placed on said image carrying member for controlling respective registrations and toner densities of said plurality of color marks on said image carrying member, one of said color marks including a polygon having a first side which is not parallel to said first and second directions.  
         [0017]     According to an aspect of the present invention, the marks are placed in margin areas of the image carrying member on opposite sides of the image carrying member.  
         [0018]     According to another aspect of the present invention, the plurality of color marks includes a plurality of color marks having a same color and different densities in series.  
         [0019]     According to another aspect of the present invention, the marks each further include a second side disposed relative to the first side in the first direction, and the apparatus further includes a control unit to determine an error of the image in the second direction by determining time intervals between the passing of the first and second sides of first and second ones of the marks on opposite sides of the image carrying member, and subtracting the determined time intervals.  
         [0020]     According to another aspect of the present invention, the apparatus further includes a sensor to detect the marks, wherein a power of an output of the sensor rises as each of the marks approaches the sensor, remains constant as each of the marks passes the sensor, and falls as each of the marks moves away from the sensor, wherein a position of the mark W relative to the sensor is determined according to W=T width /2, wherein T width  is a time between a middle time of the rising of the power of the output and a middle time of the falling of the power of the output.  
         [0021]     According to another aspect of the present invention, the sensor includes an emitter to emit a beam on the marks to detect the marks, the beam having a spot size of less than 200 microns. The spot size may even be less than 100 microns.  
         [0022]     According to another aspect of the-present invention, the apparatus further includes a Low Pass Filter to filter noise signals of the output of the sensor.  
         [0023]     According to another aspect of the present invention, the apparatus is a tandem printer including a plurality of photosensitive drums to respectively form the plurality of colors of the image.  
         [0024]     According to another aspect of the present invention, the polygon further includes a borderline at the first side, the borderline having a greater density than a non-borderline portion of the polygon.  
         [0025]     According to another aspect of the present invention, the plurality of color marks includes a plurality of color marks having different colors and same densities in series.  
         [0026]     According to another aspect of the present invention, the polygon is a trapezoid.  
         [0027]     According to another aspect of the present invention, the polygon is a wedge.  
         [0028]     According to another aspect of the present invention, said image forming apparatus further places a background toner pattern having a color other than black on the image carrying member, and the plurality of color marks comprise a mark having a black color.  
         [0029]     According to another aspect of the present invention, said emitted beam has a singular wave.  
         [0030]     According to another aspect of the present invention, said emitted beam is diffusely radiated.  
         [0031]     The foregoing and/or other aspects of the invention are also achieved by providing an apparatus to control both of color registration and color toner density at the same time in a color image forming device, said color image forming device having an image carrying member to carry an image having a plurality of colors that moves in a first direction, and perpendicular to a second direction, the apparatus including a plurality of developing units to form a plurality of color marks formed of respective colors along said first direction, said color marks forming a closed area filled with said respective one of said plurality of colors and including a first side which is not parallel to said first and second directions, wherein said respective color toner densities of said plurality of color marks are different, a sensing unit including a sensor to radiate light beams onto said color marks, to receive said light beams reflected from said color marks and to produce detection signals in accordance with the received reflected light beams, and a control unit to produce color registration offset information and color density offset information from said detection signals  
         [0032]     The foregoing and/or other aspects of the invention are also achieved by providing a method including moving an image carrying member to carry an image having a plurality of colors in a first direction; forming a plurality of polygons on the image carrying member including shading in the polygons with a toner; and sensing the polygons to determine an offset of the polygons in the first direction or a second direction perpendicular to the first direction, a skew of the polygons, or an error of the image in the second direction, the polygons including a first side which is not parallel to the first and second directions  
         [0033]     The foregoing and/or other aspects of the invention are achieved by providing in an image forming apparatus having an image carrying member for carrying thereon an image having a plurality of colors, said image carrying member being configured to move in a first direction substantially perpendicular to a second direction, a plurality of color marks having different densities being placed on said image carrying member for controlling respective registrations and toner densities of said plurality of color marks on said image carrying member, one of said color marks including a polygon having first and second opposite sides which are not parallel to each other.  
         [0034]     The foregoing and/or other aspects of the invention are also achieved by providing an apparatus to control both of color registration and color toner density at the same time in a color image forming device, said color image forming device having an image carrying member to carry an image having a plurality of colors that moves in a first direction, and perpendicular to a second direction, the apparatus including a plurality of developing units to form a plurality of color marks formed of respective colors along said first direction, said color marks forming a closed area filled with said respective one of said plurality of colors and including first and second opposite sides which are not parallel to each other, wherein said respective color toner densities of said plurality of color marks are different, a sensing unit including a sensor to radiate light beams onto said color marks, to receive said light beams reflected from said color marks and to produce detection signals in accordance with the received reflected light beams, and a control unit to produce color registration offset information and color density offset information from said detection signals.  
         [0035]     The foregoing and/or other aspects of the invention are also achieved by providing a method including moving an image carrying member to carry an image having a plurality of colors in a first direction; forming a plurality of polygons on the image carrying member including shading in the polygons with a toner; and sensing the polygons to determine an offset of the polygons in the first direction or a second direction perpendicular to the first direction, a skew of the polygons, or an error of the image in the second direction, the polygons including first and second opposite sides which are not parallel to each other 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0036]     These and/or other aspects and advantages of the invention will become apparent and more readily appreciated from the following description of the preferred embodiments, taken in conjunction with the accompanying drawings of which:  
         [0037]      FIG. 1  is a diagram of a conventional color registration sensor and mark pattern;  
         [0038]      FIG. 2  is a diagram of a conventional mark to detect image density;  
         [0039]      FIG. 3  is a block diagram of an apparatus to control color registration and image density according to an embodiment of the present invention;  
         [0040]      FIG. 4A  illustrates the mark pattern of  FIG. 3 ;  
         [0041]      FIG. 4B  illustrates another example of a mark according to the embodiment of the present invention;  
         [0042]      FIG. 5  is a sectional view of a printer in which an apparatus to control color registration and image density according to the embodiment of the present invention is installed;  
         [0043]      FIG. 6  is a sectional view of the optical module configuration of a registration and image density sensor used in the embodiment of  FIG. 3 ;  
         [0044]      FIG. 7  is a diagram of a beam radiated from the color registration sensor according to the present invention;  
         [0045]      FIG. 8  is a schematic diagram of the scattered waveform of a beam which is detected by the color registration and image density sensor according to the present invention;  
         [0046]      FIG. 9  is a diagram of signals produced with respect to marks of different colors and a same image density;  
         [0047]      FIG. 10  shows offsets calculated by the color registration and image density sensor;  
         [0048]      FIG. 11A  shows an arrangement of the marks according to color and image density according to the embodiment of the present invention;  
         [0049]      FIG. 11B  shows another arrangement of the marks according to color and image density according to the embodiment of the present invention. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT  
       [0050]     Reference will now be made in detail to the present preferred embodiment of the present invention, an example of which is illustrated in the accompanying drawings, wherein like reference numerals refer to like elements throughout.  
         [0051]      FIG. 3  is a block diagram of an apparatus to control color registration and image density according to an embodiment of the present invention. Referring to  FIG. 3 , the apparatus includes two color registration and image density sensors provided on the left and right sides and a pair of color registration and image density mark patterns (hereinafter “mark patterns” or individually as “marks”) provided on the left and right sides.  
         [0052]     A first registration and image density sensor includes a first optical module  201 , a first light emitter control unit  203 , a first color registration control unit  205 , a first image density control unit  206 , and a system control unit  207 . A second registration and image density sensor includes a second optical module  202 , a second light emitter control unit  204 , a second color registration control unit  209 , a second image density control unit  210 , and the system control unit  207 .  
         [0053]     The first and second optical modules  201  and  202  include light emitters to radiate beams onto first and second mark patterns  220  and  222 , respectively, and light receivers to receive beams reflected from the first and second mark patterns  220  and  222 , respectively. The light emitters include light sources  201 - 1  and  202 - 1 , respectively, to generate and emit light beams, and focusing lenses  201 - 2  and  202 - 2 , respectively, to focus the beams emitted from the respective light sources  201 - 1  and  202 - 1  onto the first and second mark patterns  220  and  222 , respectively. Laser diodes are used as the light sources  201 - 1  and  202 - 1 .  
         [0054]     The light receivers include photodetectors  201 - 3  and  202 - 3 , respectively, to receive the emitted beams and perform photoelectric conversion, and focusing lenses  201 - 4  and  202 - 4 , respectively, to focus the light beams emitted from the respective light emitters and reflected from the respective first and second mark patterns  220  and  222  onto the photodetectors  201 - 3  and  202 - 3 , respectively.  
         [0055]     The first and second light emitter control units  203  and  204  detect the amount of light emitted from the respective light emitters and control the light emitters to maintain a constant emission. Each of the first and second light emitter control units  203  and  204  includes a first AMP  203 - 3  or  204 - 3  to amplify a signal representing the amount of light of beams emitted from the light source  201 - 1  or  202 - 1 , and an emitted light measurer  203 - 1  or  204 - 1  to receive an output signal of the first AMP  203 - 3  or  204 - 3  and measure the amount of light emitted from each of the light emitters. The first and second light emitter control units  203  and  204  each further include a second AMP  203 - 4  or  204 - 4  to amplify an emitted light amount signal output from the emitted light measurer  203 - 1  or  204 - 1 , and a light emitter driver  203 - 2  or  204 - 2  to receive the output signal of the second AMP  203 - 4  or  204 - 4  and to control the amount of light emitted from each of the light emitters.  
         [0056]     Current signals produced by the respective light receivers are transmitted to the first and second color registration control units  205  and  209 , respectively, and to the first and second image density control units  206  and  210 , respectively. The first and second color registration control units  205  and  209  obtain information to compensate for color registration errors from the current signal produced by the respective light receivers.  
         [0057]     The first and second color registration control units  205  and  209  include I/V converters  205 - 4  and  209 - 4  to convert the current signals produced by the respective light receivers into voltage signals, AMPs  205 - 1  and  209 - 1  to amplify the voltage signals from the respective I/V converters  205 - 4  and  209 - 4 , LPFs (Low Pass Filters)  205 - 5  and  209 - 5  to pass only low frequency bands of the respective amplified signals, mark position detectors  205 - 2  and  209 - 2  to detect the positions of the first and second mark patterns  220  and  222  from signals received from the respective LPFs  205 - 5  and  209 - 5 , and offset calculators  205 - 3  and  209 - 3  to calculate offsets from the values of the respective detected mark positions. Here, the offsets include information about X-offset, Y-offset, printing width error, and skew.  
         [0058]     The first and second image density control units  206  and  210  include I/V converters  206 - 4  and  210 - 4  to convert the current signals produced by the respective light receivers into voltage signals, AMPs  206 - 1  and  210 - 1  to amplify the voltage signals from the respective I/V converters  206 - 4  and  210 - 4 , LPFs  206 - 5  and  210 - 5  to pass only low frequency bands of the respective amplified signals, image density detectors  206 - 2  and  210 - 2  to detect image density attributes for different colors from output signals of the respective LPFs  206 - 5  and  210 - 5 , and deviation calculators  206 - 3  and  210 - 3  to compare the detected image density attributes with reference image density attributes and to calculate the deviation.  
         [0059]     The system control unit  207  includes a printer controller  207 - 2  to receive information to compensate for color registration error and image density error from the first and second color registration control units  205  and  209  and the first and second image density control units  206  and  210 , and to control a printer  208 , and an offset controller  207 - 1  to change the output values of the AMPs  205 - 1  and  206 - 1  to compensate for a difference in the amount of light of beams reflected from the first and second mark patterns  220  and  222 . The system control unit  207  also includes an offset controller  207 - 3  to change the output values of the AMPs  209 - 1  and  210 - 1  to compensate for a difference in the amount of light of beams reflected from the first and second mark patterns  220  and  222 .  
         [0060]      FIG. 4A  shows the mark patterns  220 ,  222  of  FIG. 3 . Referring to  FIG. 4A , first through third image areas  224 - 1 ,  224 - 2 , and  224 - 3  are disposed in the middle of a transfer belt  240 . The mark patterns  220 ,  222  are arranged in a cross-scan direction (indicated by the arrow) on each of the right and left sides of the transfer belt  240 . The mark patterns  220 ,  222  are formed in margin areas of the transfer belt  240 .  
         [0061]     Each of the marks of the mark patterns  220 ,  222  is a shaded polygon having a side which is parallel to the scan direction, a side which is parallel to the sub-scan direction, and a slanting side which is not parallel to either of the scan or sub-scan directions. Although FIGS.  3  and  4 A illustrate a wedge-shaped polygon, other shapes are also possible, provided there is at least one side which is not parallel to the scan or sub-scan directions. For example,  FIG. 4B  illustrates a trapezoid in which the opposite sides A and B are not parallel to each other, but side B is parallel to the sub-scan direction.  FIG. 4B  also illustrates borders ‘b’ having a greater density than other portions of the marks, to improve detection of the marks.  
         [0062]     Color registration and image density sensors  221  and  223  are provided above the transfer belt  240 . Each of the color registration and image density sensors  221  and  223  radiates a beam onto a portion of the mark patterns  220 ,  222  when the mark patterns  220 ,  222  pass the respective sensor  221  or  223  as the transfer belt  240  moves in the cross-scan direction and produces a detection signal.  
         [0063]      FIG. 5  is a sectional view of a printer in which an apparatus to control color registration and image density according to the embodiment of the present invention is installed. Referring to  FIG. 5 , a color registration and image density sensor  250  (identical to sensors  221  and  223 ) is provided between an LSU  258  and a transfer roll  251 . A tof/weaving sensor  257  is provided between a charger (not shown) and the LSU  258 . Here, reference numeral  253  denotes a belt drive roll, reference numeral  255  denotes a dry/fixing device, and reference numeral  252  denotes an intermediate transfer belt. Reference number  259  is a photosensitive drum to be scanned by the LSU  258  to form a latent electrostatic image thereon. The latent electrostatic image is then developed by developer transferred via developer roll  254 . Each of the developer rolls  254  provides a different color developer, i.e., yellow, black, cyan and magenta. Thus a tandem-style printing apparatus is illustrated. However, this is just an example, and other style printers are possible.  
         [0064]     In the case where a black mark is provided, a background toner pattern of a color other than black is provided.  
         [0065]      FIG. 6  is a sectional view of the optical module configuration of a color registration and image density sensor used in the embodiment of  FIG. 3 . Referring to  FIG. 6 , an optical module  130  is provided with a light emitter including a laser diode  111  as a light source and a focusing lens  117  to focus beams emitted from the laser diode  111  onto a mark of the mark patterns  220 ,  222 . A collimating lens  113  to convert beams emitted from the laser diode  111  into parallel beams is further provided on the optical path between the laser diode  111  and the focusing lens  117 . The laser diode  111  may not focus beams on the mark patterns  220 ,  222 , but may diffusely radiate beams to detect beams reflected therefrom.  
         [0066]     Referring to  FIG. 7 , a spot size of a beam radiated onto the marks is no greater than about 200 μm. If the size of the spot is decreased to 100 μm or less, detection performance can be improved. The sensor can be made more reliable if the beam is reflected only at a position where it meets the marks. In addition, errors caused by chromatic aberration can be reduced if the emitted beam has a single wavelength.  
         [0067]     The optical module  130  further includes a light receiver including a photodetector  115  to receive beams reflected from the mark and perform photoelectric conversion, and a focusing lens  117  provided between the mark and the photodetector  115  to focus beams reflected from the mark onto the photodetector  115 .  
         [0068]     Referring to  FIG. 7 , when the mark shifts, the spot of the beam emitted from the light source shifts, as shown in the drawing. When the spot of the emitted beam is at the center of the mark, a maximum detection signal can be obtained. For optimum performance, the light receiver is designed to receive only beams diffusely reflected, rather than beams regularly reflected at an angle equal to the angle of incidence, thereby reducing detection error.  
         [0069]      FIG. 8  is a diagram of a waveform of a beam detected by the color registration and image density sensor.  FIG. 8  is provided to explain a method of detecting the position of a mark. Referring to  FIG. 8 , it can be seen from the waveform of a detection signal of beams reflected from a mark that the power of the detection signal output from a color registration and image density sensor rises as the mark on the transfer belt approaches the color registration and image density sensor, remains constant as the mark passes the center of the sensor, and gradually falls as the mark moves away from the sensor.  
         [0070]     The time taken for the power to rise from the minimum to the maximum value is represented by T rising , and the time taken for the power to fall from the maximum value to the minimum value is represented by T falling . Times T rising  and T falling  depend on the spot size of the beam. As the spot size of the beam is smaller, times T rising  and T falling  decrease, so that a mark detection error decreases.  
         [0071]     Here, the position W of the mark is determined by Formula (1). T width  indicates the time between the middle of the time T rising  and the middle of the time T falling . 
 
 W=T   width /2   (1) 
 
         [0072]      FIG. 9  is a diagram of signals produced with respect to marks of different colors and a same image density. Referring to  FIG. 9 , it can be seen from a graph of a first detection signal that the first detection signal output from the color registration and image density sensor includes a scan direction signal component and a slanting direction signal component respectively corresponding to a slanting side and a scan direction side of a first mark  120 - 1 . Masking is performed to prevent signals of second through fourth marks  120 - 2 ,  120 - 3 , and  120 - 4  from being produced. The graphs of second through fourth detection signals of the second through fourth marks can be explained in the same manner as the graph of the first detection signal.  FIG. 10  shows the marks in pairs  120 - 5 ,  120 - 6 ,  120 - 7  and  120 - 8 .  
         [0073]     Here, T y2  indicates the time interval between the scan side of the first mark  120 - 1  and the scan side of the second mark  120 - 2 . T y3  indicates the time interval between the scan side of the first mark  120 - 1  and the scan side of the third mark  120 - 3 . T y4  indicates the time interval between the scan side of the first mark  120 - 1  and the scan side of the fourth mark  120 - 4 .  
         [0074]     X-offset, that is, scan direction error, with respect to the marks can be obtained from the differences between time intervals between the scan sides and the slanting sides of the respective marks.  
         [0075]     An X-offset with respect to the second mark on the left side is expressed by Formula (2). Here, T xs1  indicates the time interval between the scan side of the first mark on the left side and the slanting side thereof, and T xs2 , T xs3 , and T xs4  indicate the same time interval with respect to the second, third and fourth marks, respectively, on the left side. 
 
T xs1 −T xs2    (2) 
 
         [0076]     When Formula (2) gives a negative result, T xs2  is greater than T xs1 , which means that the second mark on the left side is positioned further to the left than the first mark on the left side. In this case, scan direction error can be reduced by increasing the X-offset. When Formula (2) gives a positive result, T xs2  is less than T xs1 , which means that the second mark on the left side is positioned further to the right than the first mark on the left side. In this case, scan direction error can be reduced by decreasing the X-offset.  
         [0077]     X-offsets of the third and fourth marks on the left can be described in the same manner. The X-offset of the third mark on the left is expressed by Formula (3), and the X-offset of the fourth mark on the left is expressed by Formula (4). 
 
T xs1 −T xs3    (3) 
 
T xs1 −T xs4    (4) 
 
         [0078]     The same principles can be applied to the second through fourth marks on the right.  
         [0079]     Y-offset, that is, cross-scan direction error, of marks is calculated from the difference between predetermined time intervals between the scan sides of the respective marks arranged in a cross-scan direction and detected time intervals therebetween.  
         [0080]     A Y-offset of the second mark on the left is the difference between T y2  (shown in  FIG. 9 ) and T ys12  (shown in  FIG. 10 ), and is expressed by Formula (5). Here, T ys12  indicates a detected time interval between the scan side of the first mark on the left and the scan side of the second mark on the left. T ys12  is a predetermined value, but T ys12  is a variable. 
 
T y2 −T ys12    (5) 
 
         [0081]     When the Y-offset is negative, T ys12  is greater than T yx2 , that is, the detected time interval is longer than the predetermined time interval. This means that a page is delayed. Accordingly, cross-scan direction error can be reduced by advancing the page. When the Y-offset is positive, it can be inferred that a page is advanced based on the above principle. Accordingly, cross-scan direction error can be reduced by delaying the page.  
         [0082]     Y-offset of the third and fourth marks on the left can be described based on the same principles as described above. The Y-offset of the third mark on the left is expressed by Formula (6), and the Y-offset of the fourth mark on the left is expressed by Formula (7). 
 
T y3 −T ys13    (6) 
 
T y4 −T ysa4    (7) 
 
         [0083]     The same principles can be applied to the second through fourth marks on the right.  
         [0084]     Printing width error can be obtained from the difference between a first differential value and a second differential value. Each of the first and second differential values is the difference between the time interval between the scan side and the slanting side of a mark on the left, and the time interval between the scan side and the slanting side of a mark of the same color on the right.  
         [0085]     A printing width error of the second mark pair  120 - 6  is expressed by Formula (8). 
 
( T   xs1   −T   xe1 )−( T   xs2   −T   xe2 )   (8) 
 
         [0086]     When Formula (8) gives a negative result, the printing width between the second left and right marks is greater than the printing width between the first left and right marks. In this case, reduction of the printing width is required. When Formula (8) gives a positive result, the opposite is true. The same principles as described above can be applied to printing width errors of the third and fourth left and right marks. Here, T xe1  indicates the detected time interval between the scan side and the slanting side of the first mark on the right, and T xe2 , T xe3 , and T xe4  indicate the same time intervals with respect to the second through fourth marks on the right.  
         [0087]     Printing width error of the third left and right marks is expressed by Formula (9), and printing width error of the fourth left and right marks is expressed by Formula (10). 
 
( T   xs1   −T   xe1 )−( T   xs3   −T   xe3 )   (9) 
 
( T   xs1   −T   xe1 )−( T   xs4   −T   xe4 )   (10) 
 
         [0088]     Skew can be obtained from the difference between a detected time interval between the scan sides of two different marks arranged in a cross-scan direction on the left, and a detected time interval between the scan sides of corresponding two different marks arranged in a cross-scan direction on the right.  
         [0089]     Skew with respect to the second left and right marks is expressed by Formula (11). Even when the above three kinds of errors do not arise, an error in a polygon mirror in an LSU (not shown) or a laser scan error may cause a scanning line to skew. 
 
T ys12 −T ye12    (11) 
 
         [0090]     When Formula (11) gives a negative result, T ye12  is greater than T ys12 , representing skew to the right. When Formula (11) gives a positive result, skew is to the left. Here, T ys12  indicates the time interval between the scan sides of the first and second marks on the left, T ye12  indicates the time interval between the scan sides of the first and second marks on the right, T ys13  indicates the time interval between the scan sides of the first and third marks on the left, T ye13  indicates the time interval between the scan sides of the first and third marks on the right, T ys14  indicates the time interval between the scan sides of the first and fourth marks on the left, and T ye14  indicates the time interval between the scan sides of the first and fourth marks on the right. Skew with respect to the third and fourth mark pairs  120 - 7  and  120 - 8  is expressed by Formula (12) and Formula (13), respectively. 
 
T ys13 −T ye13    (12) 
 
T ys14 −T ye14    (13) 
 
         [0091]     For determining image density, the marks having a grey level of 10% for first through fourth colors are arranged in line to thus form a unit set, and consecutively, a set of marks having a grey level of 20% for the first through fourth colors are arranged in line (see  FIG. 11B ). With such an arrangement, sets of image density marks for the first through fourth colors having grey levels of 10 through 100%, increasing in steps of 10%, are arranged. Alternatively, marks having a same color and varying image densities may be printed consecutively (see  FIG. 11A ). Although  FIG. 11A  only illustrates Y and M, this process is repeated for all colors. The power of the detection signals varies with the density of the image.  
         [0092]     According to an apparatus to control color registration and image density and a method of calculating color registration error and image density error according to the embodiment of the present invention, color registration and image density can be detected using a single mark. X-offset, Y-offset, printing width error, skew and image density can be simultaneously detected and used to compensate for registration error.  
         [0093]     Although a preferred embodiment of the present invention has been shown and described, it will be appreciated by those skilled in the art that changes may be made in this embodiment without departing from the principles and spirit of the invention, the scope of which is defined in the claims and their equivalents.