Optical scanning system and image forming apparatus employing same for electrophoto graphically forming images

An optical scanning system includes a first lens for receiving a light beam from a light source and allowing the light beam to pass therethrough, and a polygon mirror having at least one reflection surface for deflecting the light beam from the first lens by reflecting the light beam on the reflection surface thereof. A second lens is provided for receiving the light beam from the polygon mirror and focusing the light beam on a first plane to be scanned. The second lens has a first surface facing toward the polygon mirror and a second surface facing toward the first plane. The first surface is of a toric shape defined by rotating, about an axis of symmetry lying in a second plane which contains an optical axis of the second lens and is parallel to a first direction in which scanning takes place, a curve lying in the second plane and having a center of curvature on the optical axis, while the second surface is of a toric aspherical shape defined by a surface-generating profile equation in which terms have respective orders equal to or greater than a fourth order with respect to the first direction. The first and second surfaces of the second lens have radii of curvature R1 and R4, respectively, in the first direction as measured from the polygon mirror along the optical axis. The radii of curvature R1 and R4 have a relationship given by .vertline.R4.vertline.<.vertline.R1.vertline..

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to an optical scanning system and also to an 
image forming apparatus, employing the same, such as, for example, a 
copier, a facsimile device, a laser beam printer or the like for 
electrophotographically forming images. 
2. Description of Related Art 
In this kind of optical scanning system, a light source is modulated by an 
image signal to emit an image-wise laser beam representing an original 
image. The laser beam emitted from the light source is directed toward a 
rotating or swivelling deflection means and is reflected or deflected 
thereby to scan the photosensitive member in a primary scanning direction. 
By so doing, the photosensitive member is exposed to the imagewise laser 
beam, while moving in a secondary scanning direction perpendicular to the 
primary scanning direction. As a result of the primary and secondary 
scannings, an electrostatic latent image corresponding to the image signal 
is formed on the photosensitive member. 
The formation of the electrostatic latent image must be conducted with high 
accuracy, and accomplishment of the image exposure of a sufficient 
resolution needs a large number of refractive forces in an image-forming 
optical unit and requires a light-flux to be shaped by the external 
configuration of a lens in the image-forming optical unit, to thereby 
control the configuration of a beam converging toward a plane to be 
scanned. These methods, however, have some inherent performance 
limitations. In view of this, the conventional optical scanning systems 
generally make use of different refractive forces in the primary and 
secondary scanning directions to compensate for shortage of the refractive 
forces, or employ a light-flux shaper corresponding to the external size 
of the lens in the image-forming optical unit to compensate for shortage 
of the force required to control the convergent beam configuration. 
To overcome such problems, an optical scanning system employing an 
odd-shaped or axially asymmetric lens in the image-forming optical unit or 
employing a light-flux shaper in the image-forming optical unit, 
particularly in a parallel light-flux portion thereof, is in practical use 
today. 
FIG. 14 schematically depicts a conventional optical scanning system having 
a surface-tilt correction function. This optical scanning system comprises 
a laser diode 101 for emitting an elliptically shaped light beam 102, a 
first image-forming optical unit 103, a polygon mirror 104 as a deflection 
means, and a second image-forming optical unit 105. The first and second 
image-forming optical units 103 and 105 are disposed upstream and 
downstream of the polygon mirror 104 with respect to the direction of 
travel of the laser beam towards a photosensitive member 106, 
respectively. Each of the first and second image-forming optical units 103 
and 105 has different refractive forces in the primary and secondary 
scanning directions. The elliptically shaped light beam 102 from the laser 
diode 101 is focused in a predetermined size on the photosensitive member 
106 by utilizing a two-step image forming function by the first and second 
image-forming optical units 103 and 105. The first image-forming optical 
unit 103 has a light-flux shaper 108 disposed in a parallel light-flux 
portion 107 of the first image-forming optical unit 103 to control the 
beam configuration so as to be focused on the photosensitive member 106. 
The optical scanning system of FIG. 14 also comprises a plurality of 
surface-tilt correction lenses disposed on a light path defined by the 
first and second image-forming optical units 103 and 105. These lenses act 
to compensate for surface tilts of a plurality of reflecting surfaces of 
the polygon mirror 104, which may be caused by an undesirable oscillatory 
or wobbling motion of a rotary shaft of the polygon mirror 104 and/or 
inaccurate assemblage of the polygon mirror 104. 
Japanese Laid-open Patent Publication (unexamined) No. 62-30214 discloses 
an optical scanning system wherein for the purpose of minimizing the 
required surface area in which various optical elements comprising the 
optical scanning system are accommodated, optics on the incident side of 
the polygon mirror and those on the reflection side of the polygon mirror 
are disposed one above the other without interfering with each other while 
an incident light path of the former forms an angle with respect to a 
reflected light path of the latter. Furthermore, the optical scanning 
system is so designed as to cause a light beam to be incident on the 
polygon mirror from the direction along the centerline of a field of scan 
in order to simplify non-uniformity of the scanning speed on a plane to be 
scanned, i.e., to make the scanning speed on such plane symmetric with 
respect to the centerline of the field of scan. Also, to reduce the 
overall size of the optical scanning system, the optics on the incident 
side of the polygon mirror includes a lens or lenses which refract the 
beam from a light source prior to the incidence thereof on the polygon 
mirror at the aforementioned angle. 
Recently, there has been an increasing demand toward a highly accurate 
image formation with high density printing. To achieve this, the use of a 
second image-forming optical unit having different sectional 
configurations in the primary and secondary scanning directions is 
preferred. 
Japanese Laid-open Patent Publication (unexamined) No. 58-93021 discloses a 
cylindrical lens employed in an optical scanning system. Although the 
formation of the cylindrical configuration is relatively easy, it is 
difficult to correct curvature of field in both the primary and secondary 
scanning directions and, hence, the use of the cylindrical lens imposes a 
limitation on the highly accurate image formation. 
Japanese Laid-open Patent Publication (unexamined) Nos. 58-179813 and 
58-179814 disclose an optical scanning system employing a troidal lens. 
The troidal surface is difficult to make because it requires forcible 
bending of the cylindrical surface, thus imposing a limitation on the 
highly accurate image formation. 
Furthermore, because each of the lenses as disclosed in the Japanese 
publications referred to above has no f-.theta. characteristics, the 
system requires an electric circuit for performing correction. 
FIGS. 15 and 16 show graphs indicating the curvature of field and an 
f-.theta. characteristic in one of the prior art references, respectively. 
In FIG. 15, a solid line indicates the curvature of field in the primary 
scanning direction, while a dotted line indicates the curvature of field 
in the secondary scanning direction. 
An alternative to achieve the highly accurate image formation with high 
density printing is to arrange a light-flux shaper such as, for example, a 
masking member having a slit in one of image-forming optical units at a 
location not affected by refraction. By so doing, it is possible to 
control the convergent beam configuration on the plane to be scanned. 
FIGS. 17A and 17B show a graph indicating the beam configuration in the 
primary scanning direction and the beam configuration in the secondary 
scanning direction in the said one of the prior art references, 
respectively. 
Japanese Laid-open Patent Publication (unexamined) No. 56-141662 discloses 
an optical scanning system wherein a masking member having a slit is 
disposed in a parallel light-flux portion. Although the installation and 
positioning of the masking member are relatively easy, the parallel 
light-flux portion must be provided in one of image-forming optical units, 
making it difficult to ensure the simplicity and reliability of the 
system. Accordingly, there is also a limitation in obtaining a highly 
accurate convergent beam. 
Japanese Laid-open Patent Publication (unexamined) No. 59-214012 discloses 
a laser printer wherein a masking member having a slit is disposed 
immediately before the plane to be scanned. This printer is at a 
disadvantage in that because the masking member must be placed remotest 
from a light source and, hence, the installation and positioning thereof 
are difficult. In addition, there is a limitation in reducing the size of 
the system. 
Furthermore, in order for the system as disclosed in the Japanese Laid-open 
Patent Publication No. 62-30214 referred to above to satisfy the 
aforementioned incidence conditions by refracting the light beam, it is 
necessary to pass the light beam through a peripheral portion of the lens 
of a large diameter, resulting in an increase in the size of the optics on 
the incident side. Although it is possible to use such a lens by removing 
an unnecessary portion thereof processing thereof takes a lot of time, 
resulting in an increase in manufacturing cost. 
The accuracy with which the light path is changed by the lenses in the 
optics on the incident side depends much upon the processing accuracy of 
the lenses themselves, and a decreased processing accuracy is likely to 
change the position of incidence on the polygon mirror, to thereby lower 
image-forming characteristics. Also, temperature changes cause a change in 
refractive index of the lens, thus changing the light path. 
SUMMARY OF THE INVENTION 
The present invention has been developed to overcome the above-described 
disadvantages. 
It is accordingly an objective of the present invention to provide an 
improved compact optical scanning system having a high resolution. 
Another objective of the present invention is to provide the optical 
scanning system of the above-described type which has a simple structure 
and can be manufactured at a low cost. 
A further objective of the present invention is to provide an image forming 
apparatus employing therein the optical scanning system referred to above. 
In accomplishing the above and other objectives, the optical scanning 
system according to the present invention comprises a light source for 
emitting a light beam, a first image-forming optical unit for receiving 
the light beam from the light source and allowing the light beam to pass 
therethrough, a deflection means having at least one reflection surface 
for deflecting the light beam from the first image-forming optical unit by 
reflecting the light beam on the reflection surface thereof, and a second 
image-forming optical unit for receiving the light beam from the 
deflection means and focusing the light beam on a first plane to be 
scanned. 
The second image-forming optical unit comprises a lens means having a first 
surface facing toward the deflection means and a second surface facing 
toward the first plane. The first surface is of a toric shape defined by 
rotating, about an axis of symmetry being parallel to a first direction in 
which scanning takes place and lying in a second plane containing an 
optical axis of the second image-forming optical unit, a curve lying in 
the second plane and having a center of curvature in alignment with a 
point on the optical axis. The second surface is of a toric aspherical 
shape defined by a surface-generating profile equation in which terms have 
respective orders equal to or greater than a fourth order with respect to 
the first direction. The first and second surfaces of the lens means have 
a radius of curvature R1 and a radius of curvature R4, respectively, in 
the first direction as measured from the deflection means along the 
optical axis, said radii of curvature R1 and R4 having a relationship 
given by: 
EQU .vertline.R4.vertline.&lt;.vertline.R1.vertline.. 
This construction can sufficiently correct not only curvature of field in 
the first direction, i.e., the primary scanning direction, but coma 
aberration in the first direction. 
Preferably, the first and second surfaces of the lens means have a radius 
of curvature R3 and a radius of curvature R5, respectively, in a second 
direction perpendicular to the first direction as measured from the 
deflection means along the optical axis, said radii of curvature R3 and R5 
having a relationship given by: 
EQU .vertline.R3.vertline.&lt;.vertline.R5.vertline.. 
By so doing, both the curvature of field in the first direction and that in 
the second direction can be simultaneously corrected and, also, spherical 
aberration in the second direction can be corrected. 
If .vertline.R3.vertline.&lt;.vertline.R4.vertline., both the curvature of 
field in the first direction and curvature of scan can be sufficiently 
corrected. 
If .vertline.R1.vertline.&lt;.vertline.R5.vertline., the curvature of field in 
the first direction and that in the second direction can be both 
simultaneously corrected, and the curvature of scan can be sufficiently 
corrected. 
If .vertline.R5.vertline. is infinity, not only the curvature of field in 
the first direction, but that in the second direction can be 
simultaneously corrected, and the curvature of scan can be sufficiently 
corrected. Furthermore, the surface shape of the lens means can be 
simplified. 
Preferably, each of the first and second image-forming optical units 
comprises a single lens, making it possible to reduce the number of parts 
and simplify the system. 
Advantageously, the reflection surface of the deflection means is of either 
a spherical shape or a cylindrical shape. Such a surface shape can widen 
the angle of scan and provides the deflection means with the lens effect, 
resulting in a reduction in the number of parts and simplification of the 
system. Also, the curvature of field in the first direction can be 
satisfactorily corrected. 
If image formation on the first plane is carried out by post-objective 
scanning, the second image-forming optical unit is simplified in 
construction, and the number of parts is reduced. 
Conveniently, the system further comprises a surface-tilt correction means 
for correcting surface tilts of the deflection means, which may be caused 
by an undesirable oscillatory or wobbling motion of a rotary shaft of the 
deflection means and/or inaccurate assemblage of the deflection means. The 
provision of the surface-tilt correction means enables properly positioned 
image formation with high accuracy. 
In another aspect of the present invention, the lens means of the second 
image-forming optical unit is so positioned as to satisfy a relationship 
given by: 
EQU 0.60&lt;M/L&lt;0.85, 
where L indicates the distance between the reflection surface of the 
deflection means and the first plane along the optical axis, and M 
indicates the distance between the reflection surface of the deflection 
means and the first surface of the lens means along the optical axis. 
Such arrangement contributes to sufficiently correcting the curvature of 
field in the first direction and, also, to correcting unevenness of scan 
and curvature of scan. 
Advantageously, a masking member having a slit defined therein is disposed 
in the proximity of a focal point of the second image-forming optical unit 
on the side of the deflection means. 
In a further aspect of the present invention, an optical scanning system 
comprises a light source for emitting a generally flat light beam, a first 
image-forming optical unit comprising a single lens for shaping and 
converging the light beam from the light source, and a deflection means 
having at least one reflection surface for deflecting the light beam from 
the first image-forming optical unit by reflecting the light beam on the 
reflection surface thereof. The optical scanning system also comprises a 
second image-forming optical unit disposed on a plane in which deflection 
of the light beam by the deflection means takes place. The second 
image-forming optical unit focuses the light beam from the deflection 
means on a photosensitive member. 
In this optical scanning system, the direction in which the light beam from 
the first image-forming optical unit is incident on the deflection means 
forms a predetermined angle with respect to the said plane, and an optical 
axis of the first image-forming optical unit is in alignment with that of 
the second image-forming optical unit as viewed from such plane. 
This optical scanning system is geometrically symmetric with respect to the 
light beam incident on the deflection means. 
Furthermore, an image forming apparatus employing therein the optical 
scanning system referred to above is compact, has a high resolution, and 
can be readily manufactured at a low cost. 
The present invention is based on the finding that in the case of the 
post-objective scanning, appropriate correction of the curvature of field, 
easy and inexpensive formation of the highly precise surface shapes of the 
second image-forming optical unit, and high-accuracy image formation on 
the plane to be scanned can be accomplished by: 
(1) different sectional configurations of the second image-forming optical 
unit in the primary and secondary scanning directions and, in particular, 
surface shapes thereof on the optical axis having specific relationships 
in radius of curvature in the primary and secondary scanning directions, 
or 
(2) appropriate selection of the position of the correction lens 5 along 
the optical axis. 
The present invention is also based on the finding that easy and highly 
accurate control of the convergent beam configuration and high-accuracy 
image formation can be accomplished by arranging the slit in the proximity 
of the focal point of the second image-forming optical unit on the side of 
the deflection means, with the plane to be scanned hardly affected by 
refraction.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Referring now to the drawings, there is shown in FIG. 1 an optical 
post-objective scanning system embodying the present invention. This 
optical scanning system comprises a laser diode 1 for emitting a light 
beam therefrom, a converging lens 2 for converging the beam emitted from 
the laser diode 1, and a masking member 3 for controlling the beam 
configuration which is to be converged onto an image plane, i.e., a plane 
to be scanned. To obtain an appropriate beam configuration, the masking 
member 3 has a horizontally extending slit 3a of a proper size defined 
therein, which is particularly illustrated in FIG. 2. The masking member 
3, however, may be of a design having an adjustable slit. The beam from 
the laser diode 1, having passed through the slit 3a in the masking member 
3, is directed toward and reflected by a first reflection mirror 21 and is 
further directed toward a rotating mirror 4 employed as a deflection 
means, which is in the illustrated embodiment a polygon mirror having an 
axis of rotation 4a. The rotating mirror 4 has a plurality of side 
reflection surfaces each lying in a cylindrical plane. 
It is, however, to be noted that each of the reflection surfaces is not 
limited to the cylindrical one but may be of a spherical shape. The reason 
for this is that the beam from the laser diode 1 is focused by the 
converging lens 2 onto any one of the reflection surfaces of the rotating 
mirror 4 in one direction, i.e., the secondary scanning direction 
perpendicular to the primary scanning direction, and this causes little 
change in refractive force in the secondary scanning direction, regardless 
of the configuration of the reflection surfaces, thus causing no 
substantial differences in the principle of operation. 
The light beam reflected by the rotating mirror 4 is directed toward and 
further reflected by a second reflection mirror 22 and is incident on a 
correction lens 5. Thereafter, the beam, having passed through the 
correction lens 5, reaches a photosensitive drum 6 and is focused thereon. 
In the illustrated embodiment, the converging lens 2 and the correction 
lens 5 are employed as first and second image-forming optical units, 
respectively. 
As shown in FIGS. 3 to 5, the correction lens 5 has a first surface 5a 
facing toward the rotating mirror 4 via the second reflection mirror 22 
and a second surface 5b facing toward the photosensitive drum 6. The first 
surface 5a is of a toric shape defined by rotating, about an axis of 
symmetry 8 perpendicular to an optical axis, an arc of R1 in radius having 
a center of curvature lying in alignment with a specific point 9 on the 
optical axis. In the practice of the present invention, the correction 
lens 5 having the toric surface 5a is positioned with the axis of symmetry 
8 being parallel to the primary scanning direction and lying in a plane 
containing the optical axis. The second surface 5b is of a non-cylindrical 
shape having a sag portion from an apex thereof on the optical axis 
expressed, in the X-Y-Z coordinate system, by: 
##EQU1## 
where K, A, B, C, and D represent aspheric deformation coefficients of the 
4.sup.th, 6.sup.th, 8.sup.th, and 10.sup.th order terms, respectively. In 
FIGS. 4 and 5, TH represents the thickness of the correction lens 5 as 
measured along the optical axis, R2 the distance between the toric surface 
5a and the axis of symmetry 8 at opposite ends of the correction lens 5, 
R3 the distance between the toric surface 5a and the axis of symmetry 8 on 
the optical axis, R4 the curvature of the second surface 5b of the 
correction lens 5 on the optical axis as measured from the incident side 
in the primary scanning direction, and R5 the curvature of the second 
surface 5b on the optical axis as measured from the incident side in the 
secondary scanning direction. 
By way of example, Tables 1, 2 and 3 indicate specific numerical values, 
wherein Y0 represents an effective scanning width substantially equal to 
the width of a paper used, L the distance between the cylindrical 
reflection surface of the rotating mirror 4 and the photosensitive drum 6, 
R the curvature of the cylindrical reflection surface, and r the distance 
between the axis of rotation 4a of the rotating mirror 4 and an apex of 
the cylindrical reflection surface. Also, M represents the distance 
between the cylindrical reflection surface and the surface of incidence of 
the correction lens 5, d the distance between the surface of exit of the 
correction lens 5 and the photosensitive drum 6, and l the distance 
between the surface of incidence of the correction lens 5 and the masking 
member 3 as measured along the light path. 
TABLE 1 
______________________________________ 
YO L R r M d 
260 230 130 25 157 33 
R1 R3 R4 R5 TH l 
697.71 21.04 168.73 .infin. 
40 41 
K A B C D 
0.0 6.264 -2.495 1.362 -1.522 
.times. 10.sup.-8 
.times. 10.sup.-12 
.times. 10.sup.-16 
.times. 10.sup.-21 
______________________________________ 
TABLE 2 
______________________________________ 
YO L R r M d 
260 230 140 25 157 42 
R1 R3 R4 R5 TH l 
696.68 21.78 221.19 .infin. 
31 42 
K A B C D 
0.0 9.294 -2.161 1.133 -5.145 
.times. 10.sup.-8 
.times. 10.sup.-12 
.times. 10.sup.-16 
.times. 10.sup.-22 
______________________________________ 
TABLE 3 
______________________________________ 
YO L R r M d 
260 230 160 25 157 58 
R1 R3 R4 R5 TH l 
730.02 23.04 598.76 .infin. 
15 44 
K A B C D 
0.0 1.186 -3.249 1.764 -2.960 
.times. 10.sup.-8 
.times. 10.sup.-12 
.times. 10.sup.-16 
.times. 10.sup.-21 
______________________________________ 
According to the present invention, .vertline.R1.vertline. is so chosen as 
to be greater than .vertline.R4.vertline., or .vertline.R5.vertline. is so 
chosen as to be greater than .vertline.R3.vertline.. Preferably, 
.vertline.R3.vertline.&lt;.vertline.R4.vertline.&lt;.vertline.R1.vertline. and, 
more preferably, 
.vertline.R3.vertline.&lt;.vertline.R4.vertline.&lt;.vertline.R1.vertline.&lt;.vert 
line.R5.vertline.. Conveniently, .vertline.R5.vertline. is so chosen as to 
be infinity, as shown in Tables 1, 2, and 3 above. 
Alternatively, L and M are so chosen as to satisfy a relationship given by 
0.60&lt;M/L&lt;0.85. 
As is clear from the above and as can be readily known from FIGS. 3 to 5, 
the correction lens 5 employed as the second image-forming optical unit 
has different sectional configurations in the primary and secondary 
scanning directions, and surface shapes thereof on the optical axis have 
specific relationships in radius of curvature in the primary and secondary 
scanning directions. Alternatively, the position of the correction lens 5 
along the optical axis is properly selected. 
By so doing, not only curvature of field can be appropriately corrected, 
but also the correction lens 5 having highly precise surface shapes can be 
readily manufactured at a low cost. Also, image formation on the 
photosensitive drum 6 can be conducted with high accuracy. 
The operation of the optical post-objective scanning system referred to 
above is discussed hereinafter with reference to FIGS. 6A and 6B depicting 
the light path in a plane lying in the primary scanning direction and in a 
plane lying in the secondary scanning direction, respectively. 
The light beam emitted from the laser diode 1 is converged by the 
converging lens 2 so as to be focused on two different points lying in the 
primary and secondary scanning directions, respectively. In the secondary 
scanning direction, the beam from the laser diode 1 converges in the 
neighborhood of the reflection surface of the rotating mirror 4. The 
rotating mirror 4 rotates about the axis of rotation 4a and deflects the 
beam incident thereon, which is in turn focused onto the photosensitive 
drum 6 by the correction lens 5 for scanning. At this moment, the beam 
focused on the plane to be scanned is controlled to a predetermined size 
in the secondary scanning direction and disorder of the configuration 
thereof is simultaneously corrected by regulating the area of the slit 3a 
in the masking member 3. To this end, the masking member 3 is disposed in 
the proximity of a focal point of the correction lens 5 in the secondary 
scanning direction. Because the correction lens 5 is disposed so that a 
deflection or reflection point thereon and that portion of the 
photosensitive drum 6 which is to be scanned are geometrically conjugate 
to each other in the secondary scanning direction, the correction lens 5 
acts to correct surface tilts of the rotating mirror 4 and also correct 
curvature of field in the secondary scanning direction by reducing the 
refractive force in the secondary scanning direction as the location on 
which the reflected beam from the rotating mirror 4 is incident is brought 
near any of the opposite ends of the correction lens 5 in the primary 
scanning direction. Furthermore, an imaging position on the plane to be 
scanned in the primary scanning direction is caused to have an appropriate 
f-.theta. characteristic by rendering the surface of exit of the 
correction lens 5 to be of a non-cylindrical shape having a fourth order 
and higher order terms. 
It is however to be noted that the surface of exit of the correction lens 5 
may be of a toric aspherical shape. 
FIGS. 7 and 8 show a graph indicating the curvature of field and a graph 
indicating the f-.theta. characteristic of the optical scanning system 
referred to above, respectively. In the graph of FIG. 7, a solid line 
indicates the curvature of field in the primary scanning direction, while 
a dotted line indicates that in the secondary scanning direction. FIGS. 9A 
and 9B depict the beam configuration in the primary scanning direction and 
that in the secondary scanning direction, respectively. 
As described hereinabove, according to the present invention, the use of 
the rotating mirror 4 in the form of a polygon as the deflection means is 
effective in correcting the curvature of field in the primary scanning 
direction. Also, the use of the correction lens 5 is effective in 
correcting the curvature of field in the primary scanning direction and in 
simultaneously correcting the curvature of field in the secondary scanning 
direction with an appropriate f-.theta. characteristic given to the 
imaging position. In addition; the beam focused on the plane to be scanned 
is controlled to a predetermined size in the secondary scanning direction 
and disorder of the configuration thereof is simultaneously corrected by 
regulating the area of the slit 3a in the masking member 3, as described 
above. 
FIG. 10 depicts an image forming apparatus employing the optical scanning 
system discussed above. 
The image forming apparatus of FIG. 10 comprises a photosensitive drum 31 
and an optical scanning system 32 of the present invention disposed above 
the photosensitive drum 31. A first charger 33, a developing unit 34, a 
transfer charger 35, and a cleaner 36 are disposed around the 
photosensitive drum 31 in this order in a direction of rotation of the 
photosensitive drum 31. A pre-exposure lamp 37 is disposed obliquely above 
the photosensitive drum 31, while a fixing unit 38 and a paper cassette 39 
are disposed on opposite sides of the photosensitive drum 31. 
It is to be noted that the present invention is applicable not only to the 
optical post-objective scanning system but to an optical pre-objective 
scanning system. Even in the latter, the effects of the present invention 
can be obtained in both the primary and secondary directions. 
It is also to be noted that although the converging lens 2 is a single lens 
constituting the first image-forming optical unit while the correction 
lens 5 is a single lens constituting the second image-forming optical 
unit, at least one of the first and second image-forming optical units can 
be made up of a plurality of lenses. 
FIG. 11 depicts an optical scanning system according to a second embodiment 
of the present invention. This optical scanning system is in most cases 
incorporated in a frame 41 as shown in FIG. 12. The frame 41 is made of, 
for example, a highly accurate molded article. 
As shown in FIGS. 11 and 12, a rotating mirror 42 in the form of a polygon 
and a single lens 45 constituting the first image-forming optical unit are 
mounted on the frame 41 in a spaced relationship. The rotating mirror 42, 
employed as a deflection means, is disposed on one side of the frame 41 
and is accurately mounted on a spindle 44 of a high-speed drive motor 43. 
The rotating mirror 42 has a plurality of reflection surfaces each of a 
cylindrical shape in a direction of rotation thereof, thereby providing 
the reflection effect and the lens effect. 
Held by a lens holder 46, the single lens 45 is fixed on the frame 41 at a 
central portion thereof. A laser holder 48 having a laser diode 47 as a 
light source pressed thereinto is mounted on one end of the lens holder 
46, while a masking member 49 having a horizontally extending slit 49a 
defined therein is mounted on the other end of the lens holder 46 to 
control the configuration of light having passed through the single lens 
45. The laser diode 47 is of a design capable of emitting an elliptically 
cross-sectioned bundle of divergent rays of light which are in turn 
converged and shaped by the lens 45. 
FIGS. 13A and 13B depict the configuration of the lens 45. As shown in 
these figures, the lens 45 has a first surface 45a and a second surface 
45b opposite to each other, each of which is of an anamorphic 
configuration having different radii of curvature in the primary scanning 
direction parallel to the direction of rotation of the rotating mirror 42 
and in the secondary scanning direction perpendicular to the primary 
scanning direction. An optical axis of the lens 45 is in alignment with 
that of the laser diode 47 so that the major and minor axes of the 
elliptically shaped beam from the laser diode 47 may extend in the primary 
and secondary directions, respectively. Furthermore, the slit 49a in the 
masking member 49 extends in the primary scanning direction, while the 
lens holder 46 is properly positioned so that outgoing light from the lens 
45 is directed to the center of the motor spindle 44 via the slit 49a and 
is incident on the rotating mirror 42 at an angle T. Because the lens 45 
is complicated in configuration, it is generally directly molded from 
glass material. 
An elongated single lens 53 constituting the second image-forming optical 
unit and having a linearity correction function is disposed opposite to 
the rotating mirror 42 in a spaced relationship from the lens 45. The lens 
53 extends in a direction perpendicular to an optical axis 54 of the first 
image-forming optical unit and is placed symmetrically with respect to 
this optical axis 54 so as to lie in a plane which the rotating mirror 42 
scans. 
The lens 53 has a first surface 53a and a second surface 53b opposite to 
each other. The first surface 53a is of a toric shape having a negative 
radius of curvature in the primary scanning direction and also having a 
positive radius of curvature in the secondary scanning direction which 
varies from the lens center. The second surface 53b is of a cylindrical 
shape having a positive radius of curvature in the primary scanning 
direction. This lens 53 has a long complicated configuration and is 
primarily made of a highly accurate resinous molded article resistant to 
heat and insusceptible to water. 
The light beam reflected at the angle T and deflected by the rotating 
mirror 42 scans a V-shaped field extending at an angle U and is incident 
on the center of the toric lens 53 in the secondary scanning direction. 
A reflection mirror 57 is disposed obliquely above the toric lens 53 to 
change or bend the light path. A beam detection sensor 59 and a beam 
detection lens 60 are disposed aside the lens 45 at a location outside the 
scan field U to obtain synchronization required to start writing or 
printing images. A cylindrical lens is preferably used for the beam 
detection lens 60. 
A photosensitive drum 58 having an axis of rotation in the primary scanning 
direction is disposed below the frame 41. The photosensitive drum 58 is 
exposed to imagewise light for subsequent formation of an electrostatic 
latent image thereon. 
The optical scanning system of the above-described construction operates as 
follows. 
Based on an image signal from the system, the laser diode 47 receives a 
video signal along with a predetermined clock signal, and a 
synchronization detection signal from the beam detection sensor 59 turns 
the laser diode 47 on. A beam emitted from the laser diode 47 passes 
through and is slightly converged by the lens 45 in the primary scanning 
direction, and is then focused by the rotating mirror 42 to a 
predetermined beam spot on the photosensitive drum 58. In the secondary 
direction, the beam from the laser diode 47 is temporarily focused on the 
rotating mirror 42 and is then diverged thereby. This divergent beam from 
the rotating mirror 42 is finally focused by the long toric lens 53 on the 
photosensitive drum 58. Because of this, the lens 45 has a large ratio of 
the focal length in the primary scanning direction to that in the 
secondary scanning direction, while the slit 49a in the masking member 49 
has a large aspect ratio, i.e., a large ratio of the long side to the 
short side. Accordingly, it is necessary to make the beam configuration 
from the lens 45 flatter than the elliptically shaped beam from the laser 
diode 47. 
Although the light beam incident on the rotating mirror 42 at the angle T 
is reflected thereby at the same angle, rotation of the rotating mirror 42 
is followed by a back-and-forth movement of the mirror surface, which in 
turn causes a vertical movement of the reflection point of the light beam 
on the rotating mirror 42, resulting in bending of the light beam focused 
on the photosensitive drum 58. Accordingly, a small angle of incidence is 
preferred. 
However, as the angle of incidence T becomes smaller, there arises an 
interference between the first and second image-forming scanning units, 
which causes the possibility of the light beam travelling in an undesired 
direction. Up to this time, the polygon mirror has been in most cases 
spaced away from the lenses of the first image-forming optical unit to the 
extent of causing no interference, resulting in an increase in size of the 
lens assembly. 
According to the second embodiment of the present invention, the use of the 
single lens 45 for the first image-forming optical unit can reduce the 
angle of incidence T without increasing the distance between the rotating 
mirror 42 and the light source, and the required image-forming 
characteristics can be obtained. 
In this embodiment, if the radius of curvature R of the polygon mirror 42, 
the radius r of an inscribed circle of the polygon mirror 42, the distance 
E between the polygon mirror 42 and the single lens 45, the distance M 
between the polygon mirror 42 and the toric lens 53 along the optical 
axis, the distance d between the photosensitive drum 58 and the toric lens 
53, the angle of incidence T, the scan angle U, the radii of curvature S1 
and S2 of the first and second surfaces 45a and 45b of the lens 45 in the 
secondary scanning direction are chosen to take the following values, 
curvature of scan on the photosensitive drum 58 can be reduced to 0.2 mm 
or smaller. 
R=140 mm, r=25 mm, E=70 mm, 
M=152 mm, d=83 mm, T=25.degree., 
U=30.degree., S1=3 mm, and S2=130 mm 
Furthermore, because the system of the present invention is so designed 
that light having passed through the lens 45 travels along the optical 
axis thereof and is then directly incident on the polygon mirror 42, the 
point of incidence on the polygon mirror 42 does not significantly change. 
This improves the image-forming characteristics and enhances the 
resolution. Also, because the optical geometry of the present invention is 
made symmetric with respect to the aforementioned optical axis, all the 
lenses used can be manufactured with ease. In addition, the single lens 45 
is molded from glass, contributing to a considerable reduction in the 
number of parts, reducing the manufacturing cost thereof, and enhancing 
the system reliability. 
As described hereinabove, according to the present invention, 
.vertline.R1.vertline. is so chosen as to be greater than 
.vertline.R4.vertline.. This relationship enables not only sufficient 
correction of curvature of field in the primary scanning direction, but 
also correction of coma aberration in the primary scanning direction, 
making the convergent beam sufficiently uniform in the primary scanning 
direction and providing the system with a high resolution. 
Furthermore, .vertline.R5.vertline. is so chosen as to be greater than 
.vertline.R3.vertline.. This relationship enables simultaneous correction 
of both the curvature of field in the first direction and that in the 
second direction and, also, enables correction of spherical aberration in 
the second direction. As a result, the convergent beam is made uniform in 
both the primary and secondary directions, to thereby provide the system 
with a high resolution. 
When .vertline.R3.vertline.&lt;.vertline.R4.vertline.&lt;.vertline.R1.vertline., 
the scanning characteristics are further improved. 
When .vertline.R5.vertline. is infinity as shown in Tables 1, 2, and 3 
above, the curvature of field in the first direction and that in the 
second direction can be both simultaneously corrected, and the curvature 
of scan can be sufficiently corrected. Furthermore, because the surface 
shape of the lens of the second image-forming optical unit can be 
simplified, the manufacturing cost thereof can be reduced. 
When the lens of the second image-forming optical unit satisfies 
0.60&lt;M/L&lt;0.85, not only the curvature of field in the first direction is 
sufficiently corrected, but also unevenness of scan and curvature of scan 
are both corrected. Accordingly, the convergent beam in the primary 
scanning direction is made satisfactorily uniform, realizing a high 
resolution and high-accuracy scanning characteristics. 
Furthermore, each of the first and second image-forming optical units 
comprises a single lens, and the reflection surface of the deflection 
means is of either a spherical shape or a cylindrical shape. These 
features of the present invention make it possible to reduce the number of 
parts and simplify the system, resulting in simplification of the system 
assemblage and adjustments, high reliability of the system, and a 
reduction in both size and cost of the system. 
The provision of the surface-tilt correction means avoids an undesirable 
oscillatory motion of a rotary shaft of the deflection means and/or 
inaccurate assemblage of the deflection means, enabling properly 
positioned image formation with high accuracy. Accordingly, the resolution 
is enhanced and the scanning characteristics are improved. Also, the 
system assemblage and adjustments are simplified and the system 
reliability is ensured. 
Furthermore, the image forming apparatus employing therein the optical 
scanning system of the present invention is compact, has a high 
resolution, and can be readily manufactured at a low cost. 
Although the present invention has been fully described by way of examples 
with reference to the accompanying drawings, it is to be noted here that 
various changes and modifications will be apparent to those skilled in the 
art. Therefore, unless such changes and modifications otherwise depart 
from the spirit and scope of the present invention, they should be 
construed as being included therein.