Image forming apparatus eliminating influence of fluctuation in speed of a conveying belt to correction of offset in color registration

An image processing apparatus eliminates a detection error in a color offset detecting operation due to a periodic fluctuation in a speed of a conveying belt which conveys a transfer sheet on which color component images are transferred and superimpose to form a multi-color image. A plurality of image forming units are arranged along the conveying belt, each of the image forming units transferring a color component image on the transfer sheet and also transferring a register mark on the conveying belt. A register mark detecting sensor located along the conveying belt detects the register mark on the conveying belt. A distance between the register mark detecting sensor and one of the plurality of image forming units adjacent to the register mark detecting sensor is a multiple of an integer of a circumference of the drive roller. A distance between adjacent ones of the plurality of image forming units is a multiple of an integer of the circumference of the drive roller.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to a multi-color image forming apparatus such 
as an electrophotographic apparatus and, more particularly, to a 
multi-color image forming apparatus in which a plurality of color 
component images are sequentially transferred and superimposed on a 
recording medium carried by a conveying belt. 
2. Description of the Related Art 
In an image forming apparatus such as a multi-color printer or a 
multi-color copy machine, a plurality of image forming units are serially 
arranged along a conveying belt, the image forming units form color 
component toner images corresponding to yellow, magenta, cyan and black. 
Each of the color component images are transferred and superimposed on a 
transfer sheet conveyed by a conveying belt so that a multi-color or 
full-color image is formed. In the above-mentioned image forming apparatus 
such as an electrophotographic apparatus, it is required to accurately 
superimpose color component images without an offset with respect to each 
other so as to form a high-quality color image. 
Japanese Laid-Open Patent Application No. 6-18796 discloses an image 
forming apparatus which corrects a color offset with respect to a 
reference color (black, for example) by forming register marks 
corresponding to color component images on a conveying belt and detecting 
the register marks by a CCD sensor. 
Additionally, Japanese Laid-Open Patent Application No. 8-123129 discloses 
an image forming apparatus similar to the image forming apparatus 
disclosed in the above-mentioned patent document. The image forming 
apparatus disclosed in Japanese Laid-Open Patent Application No. 8-123129 
further comprises a stain preventing member which prevents formation of a 
stain on the register marks. 
Each of the above-mentioned conventional image forming apparatuses is 
structured as shown in FIG.1. That is, an image forming unit 20Y, an image 
forming unit 20M, an image forming unit 20C and an image forming unit 20K 
are arranged along a conveying belt 35 which is drivingly engaged with a 
drive roller 36 and an idle roller 37. The image forming units 20Y, 20M, 
20C and 20K form a yellow toner image, a magenta toner image, a cyan toner 
image and a black toner image, respectively. 
Additionally, a paper supply cassette 40 which stores transfer papers is 
provided under the conveying belt 35. A paper supply roller 41 which feeds 
the transfer paper is provided on an end portion of the paper supply 
cassette 40. A register roller 42 which feeds the transfer paper to the 
conveying belt 35 is provided near the image forming unit 20Y. A fixing 
roller 43 and a pressing roller 44 which fix a toner image formed on the 
transfer paper are provided near the drive roller 36. 
The image forming unit 20Y comprises a photosensitive drum 1Y, a charger 
30Y, an optical writing unit 31Y, a developing unit 32Y, a transfer unit 
33Y, and a cleaning unit 34Y. The charger 30Y charges the photosensitive 
drum 1 so that an electrostatic latent image is formed on the 
photosensitive drum 1Y by the optical writing unit 31Y. The developing 
unit 32Y develops the latent image as a yellow (Y) toner image. The Y 
toner image is transferred to transfer paper. The cleaning unit 34Y 
removes toner remaining on the photosensitive drum 1Y. 
Similarly, the image forming unit 20M comprises a photosensitive drum 1M, a 
charger 30M, an optical writing unit 31M, a developing unit 32M, a 
transfer unit 33M, and a cleaning unit 34M. The image forming unit 20C 
comprises a photosensitive drum 1C, a charger 30C, an optical writing unit 
31C, a developing unit 32C, a transfer unit 33C, and a cleaning unit 34C. 
The image forming unit 20K comprises a photosensitive drum 1K, a charger 
30K, an optical writing unit 31K, a developing unit 32K, a transfer unit 
33K, and a cleaning unit 34K. 
In the above-mentioned structure, a position offset sensor 45 is provided 
near the drive roller 36. The position offset sensor 45 detects register 
marks formed by the image forming units 20Y, 20M, 20C and 20K. A 
discharger 38 is provided on the downstream side of the position offset 
sensor 45 so as to discharge the conveying belt 35. A cleaning unit 39 is 
provided near the idle roller 37 so as to remove toner remaining on the 
conveying belt 35. 
In the above-mentioned conventional image forming apparatus, the Y toner 
image is transferred onto a transfer paper by the image forming unit 20Y 
so that the Y toner image is transferred in synchronization with the 
conveyance of the transfer paper by the transfer belt 35. The transfer 
paper having the Y toner image is conveyed to a position corresponding to 
the image forming unit 20M. Then, a magenta (M) toner image is transferred 
and superimposed on the Y toner image by the image forming unit 20M. 
Similarly, a cyan (C) toner image is transferred and superimposed on the M 
toner image and, then, a black (K) toner image is transferred on the M 
toner image. Accordingly, a multi-color or full-color image is formed by 
the superimosingly transferred Y toner image, M toner image, C toner image 
and K toner image being superimposed. The multi-color image is fixed on 
the transfer paper by being passed through a portion between the fixing 
roller 43 and the pressing roller 44. 
In the above-mentioned image forming process, register marks corresponding 
to each color of the image forming units 20Y, 20M, 20C and 20K are formed 
and developed on an area of each of the photosensitive drums 1y, 1M, 1C 
and 1K, respectively. The register marks are transferred to the conveying 
belt 35 in synchronization with a transfer operation of each of the Y, M, 
C and K toner images by the respective transfer units 33Y, 33M, 33C and 
33K. Then, the register marks in each color are read by the position 
offset sensor 45 so as to detect an offset of the register marks 
corresponding to Y, M and C with respect to K. A writing position of each 
of the optical writing units 31Y, 31M, and 31C is adjusted so as to 
correct the offset detected by the position offset sensor 45. 
In the above-mentioned conventional image forming apparatus, since the 
endless conveying belt 35 is driven by the drive roller 36, speed of the 
conveying belt 35 periodically fluctuates due to an eccentricity of the 
drive roller 36 or an eccentricity of rotational force transmitting parts 
such as a gear for transmitting a rotational force to the drive roller 36. 
When such a periodic fluctuation occurs in the speed of the conveying belt 
35, the register marks are formed at positions slightly offset from 
accurate positions in which the register marks are to be formed since the 
operation of forming the register marks is performed on the assumption 
that the conveying belt 35 is moving at a constant speed. Accordingly, the 
register marks are detected by the position offset sensor 45 at slightly 
offset positions. Thus, there is a problem in that an accurate detection 
of the offset in the positions of the register marks cannot be performed 
due to the periodic fluctuation in the speed of the conveying belt 35. 
A description will now be given of another conventional image forming 
apparatus in which a color offset is corrected by detecting a position 
offset of a register mark corresponding to each color component image. 
FIG. 2 is an illustration of a structure of a conventional color image 
forming apparatus. In FIG. 2, parts that are the same as the parts shown 
in FIG. 1 are given the same reference numerals, and descriptions thereof 
will be omitted. The color image forming apparatus shown in FIG. 2 has the 
same structure with the image forming apparatus shown in FIG. 1 except for 
the position offset sensor 45 being replaced with a register mark 
detecting sensor 14 located on the same side where the image forming units 
20Y, 20M, 20C and 20K are located. 
In the color image forming apparatus shown in FIG. 2, a recording paper 
(transfer sheet) 10 is fed onto the conveying belt 35 from the paper 
cassette 40. The recording paper 10 is secured on the conveying belt 35 by 
an electrostatic force, and conveyed to the image forming unit 20Y so that 
an yellow toner image is formed on the recording paper 10. Thereafter, a 
magenta toner image, a cyan toner image and a black toner image are 
sequentially and formed and superimposed by the respective image forming 
units 20M, 20C and 20K. After the black toner image is formed by the image 
forming unit 20K, the recording paper 10 is passed through the fixing unit 
comprising the fixing roller 43 and the pressing roller 44 so that the 
toner image on the recording paper 10 is fixed, and then the recording 
paper 10 is ejected to a paper eject tray (not shown in the figure). It 
should be noted that operations of the optical writing units 31Y, 31M, 31C 
and 31K are controlled by a control unit 53 so that the Y, M, C and K 
toner images are accurately formed on the respective photosensitive drums 
1Y, 1M, 1C and 1K. 
FIG. 3A is a perspective view of a part of the color image forming 
apparatus shown in FIG. 2. In FIG. 3A, a direction indicated by an arrow B 
(hereinafter referred to as direction B) is perpendicular to a moving 
direction of the conveying belt 35 indicated by an arrow C (hereinafter 
referred to as direction C). That is, the direction B corresponds to a 
primary scanning direction, and the direction C corresponds to a secondary 
scanning direction. In the color image forming apparatus, if a distance 
between the image forming units 20Y, 20M, 20C, and 20K or an angle of each 
of the image forming units 20Y, 20M, 20C and 20K is shifted from a correct 
position, this causes a color offset (an offset in a registration of color 
component images) in the output image and results in deterioration of the 
output image quality. Accordingly, in the color image forming apparatus, 
each of the image forming units 20Y, 20M, 20C and 20K forms a register 
mark 15 on the conveying belt 35 so that an offset in a registration of 
color component images can be detected. The correction is performed based 
on the offset in the registration of each of the color component images by 
detecting the register mark 15 formed by each of the image forming units 
20Y. 20M, 20C and 20K. The register mark 15 and the register mark 
detecting sensor 14 are shown in FIG. 3A. The register marks 15 are formed 
on each side of the conveying belt 35. Thus, the register mark detecting 
sensor 14 is provided on each side of the conveying belt 35 on the 
downstream side of the image forming unit 20K so as to detect the register 
marks 15 formed on the conveying belt 35. 
FIG. 3B is a perspective view of the register mark detecting sensor 14. 
Each of the register marks 15 comprises a mark extending in the direction 
B perpendicular to the direction C of the movement of the conveying belt 
35 and a mark inclined a predetermined angle (for example, 45 degrees) 
with respect to the direction B. Each of the register mark detecting 
sensors 14 is located in a position where the register marks 15 can be 
detected. Hereinafter, a description will be give to one of the register 
mark detecting sensors 14 since they are identical to each other. The 
register mark detecting sensor 14 detects a time when the register mark 15 
passes the position of the register mark detecting sensor 14. The register 
position offset of each register mark 15 is obtained based on the time of 
passage of each register mark 15. 
The register mark detecting sensor 14 comprises a light-emitting diode 
(LED) 14-1, a slit plate 14-2 and a light-receiving element 14-3. The LED 
14-1 is located on the side of the conveying belt 35 where the register 
mark 15 is formed so as to project a light to the register mark 15. The 
slit plate 14-2 and the light-receiving element 14-3 are located on the 
opposite side of the conveying belt 35, that is, an inner side of a loop 
formed by the conveying belt 35. The slit plate 14-2 has a slit having a 
shape the same as that of the register mark 15 so that the light projected 
from the LED 14-1 passes therethrough. The light-receiving element 14-3 
receives the light passing through the slit of the slit plate 14-2. 
Accordingly, the light-receiving element 14-3 receives the light projected 
from the LED 14-1 when the register mark 15 is not present. On the other 
hand, the light-receiving element 14-3 receives a reduced light when the 
register mark 15 passes directly above the slit plate 14-2. The 
light-receiving element 14-3 detects the time when the register mark 15 
passes by a difference in the amount of received light. 
FIG. 4A is an illustration showing a positional relationship between the 
register mark detecting sensor 14 and the register mark 15 comprising a 
pair of marks K1 and K2 formed by the image forming unit 20K (black) and a 
pair of marks C1 and C2 formed by the image forming unit 20C (cyan). When 
the mark K1 or C1 is aligned with the slit extending in the direction B, 
or when the line mark K2 or C2 is aligned with the slit inclined with 
respect to the direction B, an amount of light received by the 
light-receiving element 14-3 is minimized. FIG. 4B is a time chart showing 
a peak of a detection signal output by the register mark detecting sensor 
14. The peak indicates a time when the amount of light received by the 
register mark detecting sensor 14 is minimized. Accordingly, time TK1, 
TK2, TC1 and TC2 correspond to time when the corresponding marks K1, K2, 
C1 and C2 pass the register mark detecting sensor 14. 
An offset of a register position of the cyan toner image with respect to a 
reference color toner image (black, in this case) can be obtained by the 
following relationship, where V0 is a speed of movement of the register 
mark 15, that is, a speed of movement of the conveying belt 35; and T0 is 
a time difference between the time when the mark K1 is detected and the 
time when the mark C1 is detected. It should be noted that an angle of the 
marks K2 and C2 with respect to the respective mark K1 and C1 is 45 
degrees. 
An amount E of the offset of a position of the cyan tone image in the 
primary scanning direction (direction B) with respect to the reference 
color toner image (black) is represented by the following relationship. 
EQU E={(TC2-TC1)-(TK2-TK1)}.times.V0 (1) 
An amount F of the offset of the position of the cyan toner image in the 
secondary scanning direction (direction C) with respect to the reference 
color toner image (black) is represented by the following relationship. 
EQU F={(TC2-TC1)-T0)}.times.V0 (2) 
A description will now be given of a more specific example. It is now 
assumed that the cyan marks C1 and C2 are spaced from the respective line 
marks K1 and K2 by a distance of 30 mm in the secondary scanning direction 
so that the mark K2 (black) does not cross the mark C1 (cyan). 
Accordingly, if the marks C1 and C2 are shifted toward the marks K1 and K2 
by the distance of 30 mm, the line marks C1 and C2 coincide with the 
respective marks K1 and K2. That is, the cyan marks C1 and C2 do not have 
a position offset with respect to the black marks K1 and K2. 
In FIGS. 4A and 4B, if V0=100 mm/sec; TK1=0 sec; TK2=0.1 sec; TC1=0.3 sec; 
TC2=0.4 sec; and T0=0.3 sec, this means that a distance between marks K1 
and K2 is 10 mm; a distance between marks K1 and C1 is 30 mm; and a 
distance between marks K1 and C2 is 40 mm. In this condition, an amount of 
offset of position in the primary scanning direction and the secondary 
scanning direction can be calculated by the above relationships (1) and 
(2) as follows. 
EQU E={(0.4-0.3)-(0.1-0)}.times.100=0 mm 
EQU F={(0.3-0)-0.3}.times.100=0 mm 
As appreciated from above, no offset of position is present in both the 
primary scanning direction and the secondary scanning direction. 
FIGS. 5A and 5B correspond to FIGS. 4A and 4B, respectively, in a case when 
an offset of position is generated in both the primary scanning direction 
and the secondary scanning direction. It should be noted that, in FIGS. 5A 
and 5B, the offset of position is emphasized for the sake of easy 
recognition. 
In FIGS. 5A and 5B, if V0=100 mm/sec; TK1=0 sec; TK2=0.1 sec; TC1=0.301 
sec; TC2=0.4015 sec; and T0=0.3 sec, this means that a distance between 
marks K1 and K2 is 10 mm; a distance between marks K1 and C1 is 30.1 mm; 
and a distance between marks K1 and C2 is 40.15 mm. In this condition, an 
amount of offset of position in the primary scanning direction and the 
secondary scanning direction can be calculated by the above relationships 
(1) and (2) as follows. 
EQU E={(0.4015-0.301)-(0.1-0)}.times.100=0.05 mm=50 .mu.m 
EQU F={(0.301-0)-0.3}.times.100=0.1 mm=100 .mu.m 
As appreciated from the above, the amount E of the offset of position in 
the primary scanning direction is 50 .mu.m, and the amount F of the 
position offset in the secondary scanning direction is 100 .mu.m. 
As mentioned above, the position offset of each color register mark with 
respect to the reference color register mark can be calculated by 
detecting the time when each register mark 15 passes the register mark 
detecting sensor 14. Accordingly, an appropriate correction can be 
performed for a timing of the image forming operation so as to achieve an 
accurate registration of the register position. 
The above mentioned calculation of the amount of position offset is based 
on the assumption that the speed V0 of movement of the conveying belt 35 
is constant. However, in practice, there is a fluctuation in the speed of 
movement of the conveying belt 35 due to a fluctuation in a rotational 
speed of the drive roller or an eccentricity of the circumference of the 
drive roller with respect to the rotational axis thereof. If the speed of 
the conveying speed fluctuates, an error may be generated in the 
calculated amounts E and F of the offset of position. 
FIG. 6 is a graph of a speed V of movement in which a periodic fluctuation 
is generated. In FIG. 6, an average speed V0 of movement of the conveying 
belt 35 is 100 mm/sec, and a periodic fluctuation of about .+-.0.2 mm/sec 
is generated. 
Consideration is given to a case in which the above-mentioned marks K1, K2, 
C1 and C2 are detected when the periodic fluctuation is generated in the 
speed of movement of the conveying belt 35 as shown in FIG. 6. A 
positional relationship between the marks K1, K2, C1 and C2 is the same as 
that shown in FIG. 4A. That is, the distance between marks K1 and K2 is 10 
mm; the distance between marks K1 and C1 is 30 mm; and the distance 
between marks K1 and C2 is 40 mm. Thus, if the marks C1 and C2 are shifted 
toward the marks K1 and K2 by the distance 30 mm, the marks C1 and C2 
coincide with the respective marks K1 and K2. 
In FIG. 6, a time t when the mark K1 is detected zero (t=0), the speed V(t) 
of movement of the conveying belt 35 is represented by the following 
relationship. 
EQU V(t)=V0+V1.times.cos (.omega.t) (3) 
Where, V0=100 mm/sec; V1=0.2 mm/sec; and .omega.=2.pi./1.2 rad/sec. 
Additionally, a length L(t) of the conveying belt which passes the register 
mark detecting sensor 14 can be calculated by integrating the speed of 
movement L(t) with respect to the time. The result of the integration is 
as follows. 
EQU L(t)=V0.times.t+(V1/.omega.).times.sin (.omega.t) (4) 
With respect to the time when the marks K2, C1 and C2 are detected, the 
time should satisfy the condition such as L(t)=10 mm; L(t)=30 mm; and 
L(t)=40 mm. For example, this condition is satisfied if TK1=0 sec; 
TK2=0.09981 sec; TC1=0.29962 sec and TC2=0.39967 sec. Additionally, the 
amount of position offset is obtained by the relationships (1) and (2) as 
follows. 
EQU E=0.024 mm=24 .mu.m 
EQU F=-0.038 mm=-38 .mu.m 
As mentioned above, although the register marks shown in FIG. 4A are 
supposed to have no position offset in either the primary scanning 
direction or the secondary scanning direction, there is a detection error 
due to a fluctuation in the moving speed of the conveying belt that cannot 
be neglected. That is, there is a problem in that an error is generated 
due to a fluctuation in the moving speed of the conveying belt when an 
amount of position offset is calculated by detecting the register mark on 
the conveying belt. 
SUMMARY OF THE INVENTION 
It is a general object of the present invention to provide an improved and 
useful image forming apparatus in which the above-mentioned problems are 
eliminated. 
A more specific object of the present invention is to provide an image 
processing apparatus which eliminates a detection error in a color offset 
detecting operation due to a periodic fluctuation in a speed of movement 
of a conveying belt which conveys a transfer sheet on which color 
component images are transferred and superimposed to form a multi-color 
image. 
In order to achieve the above-mentioned objects, there is provided 
according to the present invention an image forming apparatus for forming 
a multi-color image which is formed by transferring and superimposing a 
plurality of color component images on a transfer sheet, the image forming 
apparatus comprising: 
an endless conveying belt conveying the transfer sheet, the conveying belt 
being driven by a drive roller; 
a plurality of image forming units arranged along the conveying belt, each 
of the image forming units transferring a color component image on the 
transfer sheet and also transferring a register mark on the conveying 
belt; and 
a register mark detecting sensor located along the conveying belt for 
detecting the register mark on the conveying belt, 
wherein a distance between the register mark detecting sensor and one of 
the plurality of image forming units adjacent to the register mark 
detecting sensor is a multiple of an integer of a circumference of the 
drive roller; and 
a distance between adjacent ones of the plurality of image forming units is 
a multiple of an integer of the circumference of the drive roller. 
According to the above-mentioned invention, the register mark is 
transferred on the conveying belt by the image forming units, and the 
register mark on the conveying belt is detected by the register mark 
detecting sensor. The distance from the register mark detecting sensor to 
each of the image forming units is a whole number multiple of the 
circumference of the drive roller. Thus, if there is a position offset 
when the register mark is transferred on the conveying belt due to a 
periodic fluctuation in the moving speed of the drive roller, the position 
offset is canceled when the register mark is detected by the register mark 
detecting sensor since the same position offset is present when the 
register mark detecting sensor detects the register mark. Therefore, 
influence of the periodic fluctuation in the moving speed of the conveying 
belt is automatically eliminated, resulting in a highly accurate detection 
of a color offset so as to perform an appropriate color offset correction. 
The image forming apparatus according to the present invention may further 
comprise a rotational force transmitting mechanism which includes a motor 
and an intermediate rotational member so that a rotational force of the 
motor is transmitted to the drive roller of the conveying belt via the 
intermediate rotational member, wherein the motor and the intermediate 
rotational member are rotated a multiple of an integer of turns while the 
drive roller rotates a single turn. 
According to this invention, since the motor and the intermediate 
rotational member are rotated a whole number of turns while the drive 
roller rotates a single turn, a fluctuation caused by the rotational force 
transmitting mechanism occurs in the same position of each cycle of the 
periodic fluctuation in the moving speed of the conveying belt. Thus, an 
influence of the fluctuation caused by the rotational force transmitting 
mechanism is also canceled. 
In one embodiment of the present invention, the distance between the 
register mark detecting sensor and one of the plurality of image forming 
units adjacent to the register mark detecting sensor may be equal to the 
circumference of the drive roller, and the distance between adjacent ones 
of the plurality of image forming units may be equal to the circumference 
of the drive roller. 
Additionally, the plurality of image forming units may be located on one 
side of a loop of the conveying belt, and the register mark sensor may be 
located on the other side of the loop of the conveying belt. 
There is provided according to another aspect of the present invention an 
image forming apparatus for forming a multi-color image which is formed by 
transferring and superimposing a plurality of color component images on a 
transfer sheet, the image forming apparatus comprising: 
an endless conveying belt conveying the transfer sheet, the conveying belt 
being driven by a drive roller; 
a plurality of image forming units arranged along the conveying belt, each 
of the image forming units transferring a color component image on the 
transfer sheet and also transferring a register mark on the conveying 
belt; 
a register mark detecting sensor located along the conveying belt for 
detecting the register mark on the conveying belt; and 
a control unit controlling the image forming units so that one of the image 
forming units forms a first register mark and a second register mark a 
first predetermined distance away from the first register mark and another 
one of the image forming units forms a third register mark and a fourth 
register mark so that the third register mark is formed a second 
predetermined distance away from the first register mark and the fourth 
register mark is formed a second predetermined distance away from the 
second register mark, the first predetermined distance being substantially 
equal to a distance corresponding to a n/2 rotation of the driving roller, 
n being an integer, 
wherein an amount of offset of registration of color component images 
transferred by the image forming units is determined based on an average 
value of a first amount of offset and a second amount of offset, the first 
amount of offset being detected based on a pair of the first register mark 
and the third register mark, the second amount of offset being detected 
based on a pair of the second register mark and the fourth register mark. 
According to the above-mentioned invention, the pair of the first and third 
register marks are formed the first predetermined distance away form the 
pair of second and fourth register marks. Since the first predetermined 
distance corresponds to a n/2 rotation of the driving roller, if the pair 
of the first and third register marks are formed on the plus side of a 
periodic fluctuation in the moving speed of the conveying roller caused by 
the driving roller, the pair of the second and fourth register marks are 
formed on the minus side of the periodic fluctuation. Thus, an offset due 
to the periodic fluctuation is canceled by averaging the offset obtained 
from the pair of the first and third register marks and the offset 
obtained from the pair of the second and fourth register marks. 
Accordingly, influence of the periodic fluctuation can be eliminated, 
which enables an accurate correction of a registration offset of the color 
component images. 
In one embodiment of the present invention, the first distance may 
correspond to a 1/2 rotation of the driving roller. Additionally, each of 
the first, second, third and fourth register marks comprises a first mark 
and a second mark a third predetermined distance away from the first mark, 
the first mark extending in a direction perpendicular to a direction of 
movement of the conveying belt, the second mark extending in a direction 
inclined with respect to the direction of movement of the conveying belt. 
There is provided according to another aspect of the present invention an 
image forming apparatus for forming a multi-color image which is formed by 
transferring and superimposing a plurality of color component images on a 
transfer sheet, the image forming apparatus comprising: 
an endless conveying belt conveying the transfer sheet, the conveying belt 
being driven by a drive roller in a first direction corresponding to a 
direction of conveyance of the transfer sheet; 
a plurality of image forming units arranged along the conveying belt, each 
of the image forming units transferring a color component image on the 
transfer sheet and also transferring a register mark on the conveying 
belt; 
a register mark detecting sensor unit located along the conveying belt for 
detecting the register mark on the conveying belt, the register mark 
detecting sensor unit comprising a first register mark detecting sensor 
and a second register mark detecting sensor arranged along a direction of 
movement of the conveying belt, the second register mark detecting sensor 
apart from the first register mark detecting sensor by a predetermined 
short distance; and 
a control unit controlling the image forming units so that a first register 
mark is formed by one of the image forming units and a second register 
mark is formed by another one of the image forming units so that the 
second register mark is apart from the first register mark by a distance 
substantially equal to the predetermined distance, 
wherein the first register mark and the second register mark are detected 
by the first register mark sensor and the second register mark sensor 
substantially at the same time so that an amount of offset of registration 
of color component images transferred by the image forming units is 
determined based on a time difference between a detection of the first 
register mark and a detection of the second register mark. 
According to this invention, since an amount of offset of the second 
register mark with respect to the first register mark is detected by two 
register mark detecting sensors adjacent to each other, there is less 
influence of a periodic fluctuation in a moving speed of the conveying 
belt. That is, since the amount of offset is determined based on the time 
difference between the detections of the first register mark and the 
second register mark which are also formed with a short distance 
corresponding to the distance between the register mark detecting sensors, 
influence of the periodic fluctuation which has a relatively greater 
period than the distance between the register mark detecting sensors can 
be minimized. Thus, an accurate correction of a registration offset of the 
color component images can be achieve. 
In one embodiment of the present invention, the first register mark may 
comprise a first mark extending in a second direction perpendicular to the 
first direction, a second mark extending in a direction inclined with 
respect to the first direction and a third mark extending in the second 
direction, the second mark spaced apart from the first mark by a distance 
equal to the predetermined distance of the register mark detecting sensor 
unit, the third mark spaced apart from the first mark by a distance 
corresponding to four times the predetermined short distance; 
the second register mark may comprise a fourth mark extending in a second 
direction perpendicular to the first direction, a fifth mark extending in 
a direction inclined with respect to the first direction and a sixth mark 
extending in the second direction, the fifth mark spaced apart from the 
fourth mark by a distance equal to the predetermined short distance of the 
register mark detecting sensor unit, the sixth mark spaced apart from the 
fourth mark by a distance corresponding to four times the predetermined 
short distance; and 
the fourth mark of the second register mark may be spaced apart from the 
first mark of the first register mark by a distance corresponding to two 
times the predetermined short distance.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
A description will now be given, with reference to FIGS. 7 through 12, of a 
first embodiment of the present invention. In FIGS. 7 through 12, parts 
that are the same as the parts shown in FIG. 1 are given the same 
reference numerals, and descriptions thereof will be omitted. 
FIG. 7 is an illustration of a part of an image forming apparatus according 
to the first embodiment of the present invention. In FIG. 7, a drive 
roller 36 is driven by a motor 9 via a drive roller gear 7, a gear 8a, an 
intermediate gear 8 and a motor gear 10. The motor gear 10 is formed on a 
rotatable shaft of the motor 10. The gear 8 engages the motor gear 10, and 
the gear 8a is formed on a rotatable shaft of the gear 8. The gear 8a 
engages the drive roller gear 7. In this drive roller driving mechanism, 
each of the motor 9, the motor gear 10, the intermediate gear 8 and the 
gear 8a rotate a multiple of an integer of turns while the drive roller 
36, that is, the drive roller gear 7 is rotated a complete single turn. 
Position offset sensors 22 are provided along opposite sides of the 
conveying belt 35. Each of the position offset sensor 22 comprises a light 
source such as a light-emitting diode 2, a slit plate 3 and a 
light-receiving element 4. In each of the position offset sensor 22, as 
shown in FIG. 7A, the light source 2 is located on an outer side of a loop 
of the conveying belt 35 and the slit plate 3 and the light-receiving 
element 4 are located on an inner side of the loop of the conveying belt 
35 so that the light source 2 is aligned with the slit plate 3 and the 
light-receiving element 4 via the conveying belt 35. Accordingly, the 
light source 2 is located on a side of a surface of the conveying belt 35 
on which surface the register mark 23 is transferred. 
The slit plate 3 has an opening 11 having a shape the same as that of the 
register mark 23 formed by each of the image forming units 20Y, 20M, 20C 
and 20K. The opening 11 comprises, as shown in FIG. 8, a slit 11a 
extending in a direction perpendicular to a moving direction of the 
conveying belt 35 and a slit 11b extending in a direction inclined a 
predetermined angle with respect to the slit 11a. 
Referring to FIG. 8A, in the present embodiment, the position offset sensor 
22 detects the register mark 23 formed on the conveying belt 35 by the 
image forming units 20Y, 20M, 20C and 20K at a position where an optical 
axis 22c intersects with the conveying belt 35. Additionally, each of the 
image forming units 20Y, 20M, 20C and 20K transfers the register mark 23 
on the conveying belt 35 at positions y, m, c, and k, respectively, as 
shown in FIG. 8A. Distances L1, L2, L3 and L4, which are distances from 
the optical axis 22c of the position offset sensor 22 to the respective 
positions y, m, c and k, are set to a multiple of an integer of the 
circumference D.pi. of the drive roller 36. More specifically, in the 
example of FIG. 8A, the distance L4 is set to be equal to the 
circumference D.pi. of the drive roller 36; the distance L3 is set to be a 
double of the circumference D.pi. of the drive roller 36; the distance L2 
is set to be three times the circumference D.pi. of the drive roller 36; 
the distance L1 is set to be four times the circumference D.pi. of the 
drive roller 36. 
FIG. 8B is an illustration for explaining a variation of the structure 
shown in FIG. 8A. In FIG. 8B, the position offset sensor 22 is located on 
the opposite side of the image forming units 20Y, 20M, 20C and 20K with 
respect to the conveying belt 35. The distance L4 is set to be a multiple 
of an integer of the circumference D.pi. of the drive roller 36. The 
distance L3 is set to be double the circumference D.pi. of the drive 
roller 36; the distance L2 is set to be three times the circumference 
D.pi. of the drive roller 36; the distance L1 is set to be four times the 
circumference D.pi. of the drive roller 36. 
A description will now be given of an operation for detecting a color 
offset in the present embodiment. 
If an eccentricity is present between the circumferential surface of the 
drive roller 36 and the rotational axis of the drive roller 36, a 
circumferential speed of a position of the drive roller 36 periodically 
fluctuates. This causes a periodic fluctuation in the speed of movement of 
the conveying belt 35 which is driven by the drive roller 36. 
FIG. 10A is a time chart for showing the periodic fluctuation of the speed 
of movement of the conveying belt 35 due to an eccentricity in the drive 
roller 36. The periodic fluctuation in the speed has a period T0, and has 
an amplitude A with respect to a target speed V0 of the conveying roller 
35. Accordingly, the speed V of the conveying belt 35 is represented by 
the following relationship, where .omega. is an angular velocity of the 
drive roller 36. 
EQU V=A sin (.omega.t) (5) 
A position offset .DELTA.S from a target position is generated in a 
position of the conveying belt 35 due to the periodic fluctuation in the 
speed of movement of the conveying belt 35. This fluctuation causes a 
color offset of a multi-color image which is formed by transferring and 
superimposing component toner images. The position offset .DELTA.S is 
calculated by integrating the moving speed V with respect to time t as 
follows. 
##EQU1## 
The position offset .DELTA.S is as shown in FIG. 10B. In FIG. 10B, when the 
position offset .DELTA.S is a positive value, this means that the actual 
position advances the target position. On the other hand, when the 
position offset .DELTA.S is a negative value, this means that the actual 
position follows the target position. 
For example, if a transfer of the register mark is performed at a point P1, 
the fluctuation in the speed V is zero at a time tp1 when the transfer is 
performed, but the transfer is performed in a state where the conveying 
belt 35 advances from the target position by A/.omega.. Thus, the register 
mark is formed at a position following the target position. When a 
register mark formed on the conveying belt 35 is detected at a point P2 
having a phase the same with the point P1 on the downstream side of the 
point P1, the register mark is detected by the position offset sensor 22 
by a time corresponding to the distance A/.omega. before a target time tp2 
is reached. 
Accordingly, if the register mark is transferred at the point P1 and then 
the register mark is detected at the point P2, a rearward offset of a 
transfer position of the register mark is compensated by an advance in the 
time of detection of the register mark. That is, when two points having 
the same phase are selected and a transfer of a register mark is performed 
at one of the two points and a detection of the register mark is performed 
at the other of the two points, a rearward offset of a position of the 
register mark is compensated by an advance in a time of detection of the 
register mark. Accordingly, an accurate detection of a register mark can 
be achieved without an influence from the periodic fluctuation in the 
moving speed of the conveying belt 36. 
On the other hand, if a transfer of a register mark is performed at a point 
Q1, the fluctuation in the moving speed V is zero at a time tq1 when the 
transfer is performed, but the transfer is performed in a state where the 
conveying belt 35 follows the target position by A/.omega.. Thus, the 
register mark is formed at a position in advance of the target position. 
When the register mark formed on the conveying belt 35 is detected at a 
point Q2 having a phase the same with the point P1 on the downstream side 
of the point Q1, the register mark is detected by the position offset 
sensor 22 by a time corresponding to the distance A/.omega. after a target 
time tq2 is reached. 
Accordingly, if the register mark is transferred at the point Q1 and then 
the register mark is detected at the point Q2, a forward offset of a 
transfer position of the register mark is compensated by a delay in the 
time of detection of the register mark. That is, when two points having 
the same phase are selected and a transfer of a register mark is performed 
at one of the two points and a detection of the register mark is performed 
at the other of the two points, a forward offset of a position of the 
register mark is compensated by a delay in the time of detection of the 
register mark. Accordingly, an accurate detection of a register mark can 
be achieved without an influence from the periodic fluctuation in the 
moving speed of the conveying belt 36. 
In the present embodiment, since the distances L1, L2, L3 and L4, which are 
distances from the optical axis 22c of the position offset sensor 22 to 
the respective transfer positions y, m, c and k, are set to a multiple of 
an integer of the circumference D.pi. of the drive roller 36, a phase of 
the position offset .DELTA.S of each of the transfer positions y, m, c and 
k is the same with the phase of the position offset .DELTA.S of the 
position at which the register mark 23 is detected. Accordingly, an amount 
of color offset can be accurately detected without influence of the 
periodic fluctuation in the speed of movement of the conveying belt 36 so 
as to perform an appropriate correction of the color offset. 
Additionally, since a rotational force of the motor 9 is transmitted to the 
drive roller 36 via a rotational force transmitting mechanism including 
the motor gear 10, the intermediate gear 8, the gear 8a and the drive 
roller gear 7 as shown in FIG. 11, fluctuations having a period smaller 
than the period of the periodic fluctuation are generated in the moving 
speed V of the conveying belt 35 as shown in FIG. 12. The fluctuations are 
generated due to the tolerances in the dimensions of each gear such as 
eccentricity of a pitch circle. However, in the present invention, since 
the motor 9, the motor gear 10, the intermediate gear 8 and the gear 8a 
are arranged to rotate a multiple of an integer of turns while the drive 
roller 36 rotates a single turn, a plurality of sets of the fluctuations 
having a smaller period are included in the single period of the periodic 
fluctuation of the moving speed V. Accordingly, each cycle of the moving 
speed V has the same fluctuation curve. Thus, the color offset can be 
accurately detected without influence of the fluctuations due to the 
rotational force transmitting mechanism so as to perform an appropriate 
correction of the color offset. 
As mentioned above, according to the present embodiment, an accurate 
detection of the color offset can be performed without influences of the 
periodic fluctuation in the speed of movement of the conveying belt 35 and 
an influence of fluctuations due to the rotational force transmitting 
mechanism. Since the opening 11 of the slit plate 3 comprises the slit 11a 
and the slit 11b which is inclined with respect to the slit 11a, color 
detection can be performed in both the moving direction of the conveying 
belt 35 and the direction perpendicular to the moving direction. 
A description will now be given of a second embodiment of the present 
invention. FIG. 13 is a perspective view of a part of an image forming 
apparatus according to the second embodiment of the present invention. In 
FIG. 13, parts that are the same as the parts shown in FIG. 2 are given 
the same reference numerals, and descriptions thereof will be omitted. 
In FIG. 13, two pairs 60a and 60b of register marks are formed on the 
conveying belt 35 by two of the image forming units. Each of the first 
pair 60a of the register marks the second pair 60b of the register marks 
comprises the same color marks having the same configuration. The second 
pair 60b of the register marks are apart away from the first pair 60a of 
the register marks by a distance corresponding to one half of the 
circumference of the drive roller 36 which drives the conveying belt 35. 
It should be noted that the structure of the register mark detecting 
sensor 14 is the same as that shown in FIG. 3B. 
Timing of the formation of the pairs 60a and 60b of the register marks is 
controlled by a control unit 62 in a similar manner to the control unit 53 
shown in FIG. 2. 
FIG. 14A is an illustration showing an example of a positional relationship 
between the register mark detecting sensor 14 and the pairs of the 
register marks 60a and 60b. In this example, the pair 60a of the register 
marks comprises black register marks K1a and K2a and cyan register marks 
C1a and C2a; and the pair 60b of the register marks comprises black 
register marks K1b and K2b and cyan register marks C1b and C2b. The pair 
60b of the register marks is spaced from the pair 60a of the register 
marks by a distance equal to one half of the circumference of the drive 
roller 36. FIG. 14B is a time chart of a detection signal of the register 
mark detecting sensor 14 when the register marks shown in FIG. 14A are 
detected. FIG. 14B shows that the marks K1a, K2a, C1a and C2a of the first 
pair 60a of the register marks are detected at time TK1a, TK2a, TC1a and 
TC2a; and the register marks K1b, K2b, C1b and C2b of the second pair 60b 
of the register marks are detected at time TK1b, TK2b, TC1b and TC2b. FIG. 
15 shows a fluctuation in a speed of movement of the conveying belt 35. In 
FIG. 15, the time of detection of the register marks shown in FIG. 14B is 
indicated. That is, in FIG. 15, the marks K1a, K2a, C1a, C2a, K1b, K2b, 
C1b and C2b of the pairs 60a and 60b of the register marks are detected at 
positions indicated by downward arrows. 
With regard to the first pair 60a of the register marks, it is assumed that 
the first black mark K1a is set as a reference mark and a time t when the 
black mark K1a is detected is zero (t=0). A speed Va(t) of the conveying 
belt 35 is represented by the following relationship. 
EQU Va(t)=V0+V1.times.cos (.omega.t) (7) 
A distance La(t) of travel of the conveying belt 35 passing the register 
mark detecting sensor 14 is represented by the following relationship. 
EQU La(t)=V0.times.t+(V1/.omega.).times.sin (.omega.t) (8) 
Additionally, the time when the register mark is spaced from the reference 
mark (black mark K1a) by a distance Lx corresponds to the time which 
satisfies the following relationship. 
EQU La(t)=L.times. (9) 
With regard to the second pair 60b of the register marks, it is assumed 
that the first black mark K1b is set as a reference mark and a time t when 
the black mark K1b is detected is zero (t=0). A speed Vb(t) of the 
conveying belt 35 is represented by the following relationship. 
EQU Vb(t)=V0-V1.times.cos (.omega.t) (10) 
A distance Lb(t) of travel of the conveying belt 35 passing the register 
mark detecting sensor 14 is represented by the following relationship. 
EQU Lb(t)=V0.times.t-(V1/.omega.).times.sin (.omega.t) (11) 
Additionally, the time when the register mark is spaced from the reference 
mark (black mark K1b) by a distance Lx corresponds to the time which 
satisfies the following relationship. 
EQU Lb(t)=L.times. (12) 
Each of the pairs 60a and 60b of the register marks comprises a pair of 
marks having the same color and the same configuration. Thus, the 
distances of the register marks to be detected from the reference marks 
(in this case, black marks K1a and K1b) are the same. That is, the 
distance between marks K1a and K2a is equal to the distance between marks 
K1b and K2b; the distance between marks K1a and C1a is equal to the 
distance between marks K1b and C1b; and the distance between marks K1a and 
C2a is equal to the distance between marks K1b and C2b. Accordingly, with 
respect to the corresponding marks, values of Lx in the relationships (9) 
and (12) should be equal to each other. Thus, the following relationship 
is obtained from the relationships (9) and (12). 
##EQU2## 
The obtained time t is based on the assumption that the conveying belt 35 
moves at the constant speed V0 and the time of detection does not have an 
error due to a fluctuation in the speed of movement of the conveying belt 
35. As a result, an accurate detection of a position offset can be 
performed without influence of a periodic fluctuation in the speed of 
movement of the conveying belt 35 by averaging the results of detections 
for the pairs 60a and 60b of the register marks. 
A description will now be given of a specific example of the image forming 
apparatus according to the present embodiment. 
(Specific Example 1) 
Similar to the example shown in FIG. 4A, it is assumed that the pairs 60a 
and 60b of the register marks have a positional relationship as follows: 
a distance between marks K1a and K2a is 10 mm; 
a distance between marks K1a and C1a is 30 mm; 
a distance between marks K1a and C2a is 40 mm; 
a distance between marks K1b and K2b is 10 mm; 
a distance between marks K1b and C1b is 30 mm; and 
a distance between marks K1b and C2b is 40 mm. 
In this case, for example, a result of detection for the set 60a of the 
register mark pairs may be TK1a=0 sec; TK2a=0.09981 sec; TC1a=0.29962 sec; 
TC2a=0.39967 sec. In this condition, an amount Ea of position offset in 
the primary scanning direction and an amount Fa of position offset in the 
secondary scanning direction can be calculated as follows. 
EQU Ea=0.024 mm=24 .mu.m 
EQU Fa=-0.038 mm=-38 .mu.m 
On the other hand, for example, a result of detection for the set 60a of 
the register mark pairs may be TK1b=0 sec; TK2b=0.10019 sec; TC2b=0.30138 
sec; TC2b=0.40033 sec. In this condition, an amount Eb of position offset 
in the primary scanning direction and an amount Fb of position offset in 
the secondary scanning direction can be calculated as follows. 
EQU Eb=0.024 mm=-24 .mu.m 
EQU Fb=-0.038 mm=38 .mu.m 
Accordingly, average values Eave and Fave are represented as follows. 
EQU Eave=(Ea+Eb)/2=0 (14) 
EQU Fave=(Fa+Fb)/2=0 (15) 
This result indicates that the amount of position offset coincides with 
that of the example shown in FIG. 4 which is obtained under the condition 
that there is no fluctuation in the speed of the movement of the conveying 
belt 35. 
(Specific Example 2) 
Similar to the example shown in FIG. 5A, it is assumed that the sets 60a 
and 60b of the register mark pairs have a positional relationship as 
follows: 
a distance between marks K1a and K2a is 10 mm; 
a distance between marks K1a and C1a is 30.1 mm; 
a distance between marks K1a and C2a is 40.15 mm; 
a distance between marks K1b and K2b is 10 mm; 
a distance between marks K1b and C1b is 30.1 mm; and 
a distance between marks K1b and C2b is 40.15 mm. 
In this case, for example, a result of detection for the pair 60a of the 
register marks may be TK1a=0 sec; TK2a=0.09981 sec; TC1a=0.29962 sec; 
TC2a=0.40117 sec. In this condition, an amount Ea of position offset in 
the primary scanning direction and an amount Fa of position offset in the 
secondary scanning direction can be calculated as follows. 
EQU Ea=0.074 mm=74 .mu.m 
EQU Fa=-0.062 mm =-62 .mu.m 
On the other hand, for example, a result of detection for the pair 60a of 
the register marks may be TK1b=0 sec; TK2b=0.10019 sec; TC2b=0.30138 sec; 
TC2b=0.43183 sec. In this condition, an amount Eb of position offset in 
the primary scanning direction and an amount Fb of position offset in the 
secondary scanning direction is calculated as follows. 
EQU Eb=0.026 mm=-26 .mu.m 
EQU Fb=-0.138 mm=138 .mu.m 
Accordingly, average values Eave and Fave are represented as follows. 
EQU Eave=(Ea+Eb)/2=50 .mu.m 
EQU Fave=(Fa+Fb)/2=100 .mu.m 
This result indicates that the amount of position offset coincides with the 
amount of offset of position of the example shown in FIG. 5A which is 
obtained under the condition that where is no fluctuation in the moving 
speed of the conveying belt. 
As mentioned above, an accurate amount of offset of register mark position 
can be obtained even when there is a periodic fluctuation in the speed of 
movement of the conveying belt 35 by averaging the results of detection 
for the pairs of register marks, each pair being formed spaced apart from 
each other by a distance corresponding to one half of the circumference of 
the drive roller 36 which drives the conveying belt 35. 
It should be noted that although the black register mark and the cyan 
register mark are used in the above-mentioned second embodiment, the 
present invention is not limited to these colors and shapes of the 
register mark and an accurate amount of position offset can be obtained by 
other combinations of colors or other shapes of the register mark. It is 
necessary to obtain an accurate amount of position offset so as to perform 
an accurate registration of color component images. Thus, a high quality 
color image can be obtained by an accurate registration based on the 
present invention. 
A description will now be given of a third embodiment of the present 
invention. FIG. 16A is a perspective view of a color image forming 
apparatus according to a third embodiment of the present invention. FIG. 
16B is an enlarged perspective view of a pair of register mark detecting 
sensors shown in FIG. 16A. In FIG. 16A, parts that are the same as the 
parts shown in FIG. 2 are given the same reference numerals, and 
descriptions thereof will be omitted. 
In FIG. 16A, a plurality of register marks 70 are formed on the conveying 
belt 35. Additionally, the register marks 70 are detected by a resister 
mark detecting sensor unit 71 which comprises a pair of register mark 
detecting sensors 71a and 71b. In the present embodiment, the pair of 
register mark detecting sensors 71 is provided on each side of the 
conveying belt 35. 
Specifically, as shown in FIGS. 16A and 16B, the register mark detecting 
sensors 71a and 71b are arranged along the moving direction (indicated by 
an arrow C) of the conveying belt 35. The register mark detecting sensors 
71a comprises a light-emitting diode (LED) 71a-1, a slit plate 71a-2 and a 
light-receiving element 71a-3. The LED 71a-1 is located on the side of the 
conveying belt 35 where the register marks 70 are formed so as to project 
a light to the register marks 70. The slit plate 71a-2 and the 
light-receiving element 71a-3 are located on the opposite side of the 
conveying belt 35, that is, an inner side of a loop formed by the 
conveying belt 35. The slit plate 71a-2 has a slit having a shape the same 
as that of the register mark 70 so that the a light projected from the LED 
71a-1 passes therethrough. The light-receiving element 71a-3 receives the 
light passing through the slit of the slit plate 71a-2. Accordingly, the 
light-receiving element 71a-3 receives the light projected from the LED 
71a-1 when the register mark 70 is not present. On the other hand, the 
light-receiving element 71a-3 receives a reduced light when the register 
mark 70 passes directly above the slit plate 71a-2. The light-receiving 
element 71a-3 detects the time when the register mark 70 passes by a 
difference in the amount of received light. Similarly, the register mark 
detecting sensor 71b comprises a light-emitting diode (LED) 71b-1, a slit 
plate 71b-2 and a light-receiving element 71b-3 which are arranged in the 
same manner as that of the register mark detecting sensor 71a. The 
plurality of register marks 70 are formed at intervals equal to the 
distance between the register mark detecting sensors 71a and 71b. 
Timing of the formation of the register marks 70 is controlled by a control 
unit 62 in a similar manner to the control unit 53 shown in FIG. 2. 
FIG. 17A is an illustration for explaining a positional relationship 
between the register mark detecting unit 71 and the plurality of register 
marks 70. It is assumed that the register mark detecting sensors 71a and 
71b are spaced apart from each other by a distance D; the marks K1 and K2 
are spaced apart from each other by a distance D(K1-K2); the marks C1 and 
C2 are spaced apart from each other by a distance D(C1-C2); and the marks 
K3 and C3 are spaced apart from each other by a distance D(K3-C3). In the 
present embodiment, the distances D(K1-K2), D(C1-C2) and D(K3-C3) are set 
to be equal to the distance D. FIG. 17B is a time chart of detection 
signals of the register mark detection sensors 71a and 71b when the 
register marks 70 are detected. As shown in FIG. 17B, first the mark K1 is 
detected at a time TK1a by the register mark detecting sensor 71a. 
Thereafter, the mark K1 is detected at a time TK1b by the register mark 
detecting sensor 71b when the conveying belt 35 advances the distance D. 
Additionally, substantially at the time TK1b, the mark K2 is detected at a 
time TK2a by the register mark detecting sensor 71a. Thereafter, in the 
same manner, the remainder of the marks C1, C2, K3 and C3 are detected by 
the register mark detecting sensors 71a and 71b as shown in FIG. 17B. In 
FIG. 17B, a time when each of the marks are detected by the register mark 
detecting sensor 71a is indicated as Tk1a, TK2a, TC1a, TC2a, TK3a and 
TC3a, and a time when each of the marks is detected by the register mark 
detecting sensor 71b is indicated as Tk1b, TK2b, TC1b, TC2b, TK3b and 
TC3b. 
In the present embodiment, an amount of the offset in the primary scanning 
direction (direction B) and an amount of offset in the secondary scanning 
direction (direction C) is calculated based on the detection signals 
output by the register mark detecting sensors 71a and 71b. For example, 
for the register marks 70 shown in FIG. 17A, an amount of position offset 
of the cyan mark with respect to the reference mark (black mark in this 
case) can be obtained as follows. That is, an amount E of position offset 
in the primary scanning direction is obtained by the following 
relationship. 
EQU E={(TC2a-TC1b)-(TK2a-TK1b)}.times.V0 (16) 
Additionally, an amount F of position offset in the secondary scanning 
direction is obtained by the following relationship. 
EQU F=(TK3a-TK3b).times.V0 (17) 
It should be noted that the relationship (17) represents an error with 
respect to the distance D between the register mark detecting sensors 71a 
and 71b. 
As appreciated from the relationships (16) and (17), the amounts F and F of 
the register position offset in the primary and secondary scanning 
directions are calculated based on time differences between the detection 
signals which are output at substantially the same time. Since the time 
difference is very small, an influence of a periodic fluctuation in the 
speed of movement of the conveying belt 35 is almost negligible. Thus, an 
error generated in the obtained position offset can be a small value. 
Consideration is given to an example of a set of register marks in which 
D=15 mm; D(K1-K2)=15 mm; D(C1-C2)=15.05 mm; D(K3-C3)=15.1 mm. That is, the 
amount of offset in the primary scanning direction is 
D(C1-C2)-D(K1-K2)=15.05-15=0.05 mm, and the amount of offset in the 
secondary scanning direction is D(K3-C3)-D=15.1-15=0.1 mm. 
FIG. 18 shows a moving speed of the conveying belt 35 having a periodic 
fluctuation. In FIG. 18, if the time when the mark K1 is first detected by 
the register mark detection sensor 71a is set to zero (t=0; TK1a=0), the 
time when each register mark is detected can be, for example, as follows. 
TK2a=0.14973 sec, TC2a=0.45123 sec 
TC3a=0.75127 sec, TK1b=0.14973 sec 
TC1b=0.45073 sec, TK3b=0.75027 sec 
Using the relationships (16) and (17), the amount E and F of the offsets in 
the primary and secondary scanning directions are obtained as follows. 
##EQU3## 
This results coincides with the amount of the position offset of the 
register marks. 
As mentioned above, an accurate amount of offset of register mark position 
can be obtained even when there is a periodic fluctuation in the moving 
speed of the conveying belt 35 by arranging the pair of register mark 
detecting sensors 71a and 71b along a moving direction of the conveying 
belt 35 and detecting the register marks formed at intervals corresponding 
to the distance between the register mark detecting sensors 71a and 71b so 
as to obtain the register position offset based on the time difference 
between the detection signals output from the register mark detecting 
sensors 71a and 71b. 
It should be noted that although the black register mark and the cyan 
register mark are used in the above-mentioned second embodiment, the 
present invention is not limited to these colors and shapes of the 
register mark and an accurate amount of position offset can be obtained by 
other combinations of colors or other shapes of the register mark. It is 
necessary to obtain an accurate amount of position offset so as to perform 
an accurate registration of color component images. Thus, a high quality 
color image can be obtained by an accurate registration based on the 
present invention. 
The present invention is not limited to the specifically disclosed 
embodiments, and variations and modifications may be made without 
departing from the scope of the present invention.