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BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to scanning optical systems, and particularly to a scanning optical system with less distortion (aberration).
2. Description of the Prior Art
A scanning optical system is well known in which in a laser printer or the like, a laser beam is deflected by a rotary polyhedral mirror or the like and focusing and scanning are effected on a scanning surface by an f.theta. lens. For example, Japanese Patent Application Laid-Open Nos. 5706/83 and 93021/83 disclose a simple scanning optical system which uses a single f.theta. lens. This scanning optical system has no problem when it is used for releasing characters but poses a problem of distortion due to distortion aberration when the system is used for releasing drawings. If this distortion is compensated for, the curvature of an image surface has to be sacrificed, as described in detail in the aforesaid applications.
SUMMARY OF THE INVENTION
An object of the present invention is to provide a scanning optical system in which a deviation from the f.theta. characteristic resulting from a lens constructed by rotary symmetrical surfaces of an optical axis is effectively compensated for without making the structure of an optical system complicated, and the curvature of an image surface is also excellent and scanning without distortion can be performed on the scanning surface.
The system will now be described in detail with reference to the drawings.
FIGS. 1a and 1b show an optical arrangement of a scanning optical system. FIG. 1(a) is a sectional view of a surface vertical to a scanning line, and FIG. 1(b) is a sectional view of a surface including the scanning line.
A beam emitted from a laser L enters a light deflector such as a polygon P through lenses BE1 and BE2 having a positive power which serves as a beam expander. Between the lenses BE1 and BE2 are arranged an AOM element to control ON and OFF of the light, and a cylindrical lens CY1 to converge the beam on the polygon P within FIG. 1(a). This cylindrical lens CY1 may be arranged at that position to thereby reduce a spacing between the lens BE2 and the light deflector such as the polygon P.
The light whose light path is bended by the light deflector is incident at a certain angle on an focusing element f.theta. constructed by rotary symmetrical surfaces of an optical axis and passes through a cylindrical lens CY2 to form a spot on a photosensitive drum D.
The cylindrical lens CY2 arranged at the rear of the f.theta. lens has the refractive power which establishes substantially the focusing relation between the polygon surface and the drum surface in cooperation with the f.theta. lens within the section of FIG. 1(a). This has an object of compensating for an angle of inclination of the polygon as well known.
The light from the surface of the polygon P is incident upon the cylindrical lens CY2 via the f.theta. lens. Assuming that .DELTA.S represents the curvature aberration amount of a sagittal image surface generated at the f.theta. lens and M represents the lateral focusing magnification of the cylindrical lens CY2, the curvature aberration amount .DELTA.S of the sagittal image surface on the drum is approximately expressed by the following:
.DELTA.S=M.sup.2 .DELTA.S+.DELTA.S.theta.
where .DELTA.S.theta. is the amount exclusively dependent upon the angle incident on the cylindrical lens CY2. As the incident angle increases, the .DELTA.S.theta. also increases.
The first term of the right side in the above-described equation may be made small by making M.sup.2 small. This means that the cylindrical lens CY2 is made closer toward the drum surface D. However, in the case where an electro-copying type method is used as an image forming method, for example, it is necessary to take into consideration contamination prevention of the cylindrical lens CY2 caused by powder or the like, which is a factor other than the optical design. The second term of the right side may be made small by forming a spacing between the polygon P and the f.theta. lens to use the f.theta. lens in the form of a telecentricity. However, there arises a disadvantage that the f.theta. lens increases in size.
In consideration of the foregoing, the spacings between the polygon, the f.theta. lens, the cylindrical lens CY2 and the photosensitive surface D are determined.
Even if the cylindrical lens CY2 includes a toroidal surface, the image surface curvature of a meridional surface is not so much affected as a sagittal surface. Accordingly, the meridional surface is basically controlled by the f.theta. lens but even if the sagittal surface should be deteriorated than the meridional surface in case of the individual f.theta. lens, it can be compensated for by a combination of that surface with the cylindrical lens CY2.
In the laser beam scanning optical system, the spherical aberration and comatic aberration generally involves no problem since the F number is dark, over 50.
In view of the optical performance, only the distortion remains. It is known that where the f.theta. lens is in the form of a single lens, it is difficult to minimize both the meridional surface and distortion.
According to the present invention, the f.theta. lens is designed so that the curvature of the meridional image surface is minimal, and the distortion remained at that time is compensated for by forming at least one surface of the cylindrical lens CY2 into an aspherical surface. Desirably, this aspherical surface is formed not by a cylindrical surface or a toroidal surface but by forming rotary symmetrical surfaces of an optical axis into an aspherical surface, from a viewpoint of processing method.
In addition, it is desired that the aspherical surface is satisfied with
0.05<l/f.theta.<0.5
where f.theta. is the focal length of the f.theta. lens, and l is the distance from the aspherical lens to the scanning surface.
The lower limit is provided because of the fact that if a deviation of the aspherical surface from a spherical surface excessively increases for compensating for the distortion, working becomes difficult, thus affecting also on the image surface curvature. The upper limit indicates the limit at which the aforesaid M.sup.2 acts to minimize the sagittal image surface curvature and also indicates the limit at which an error in working of the aspherical surface is not so severely required.
It is noted that the aforementioned aspherical surface is not limited to a one surface but even includes not only the case where both surfaces of the cylindrical lens CY2 are aspherical surfaces but the case where a plurality of CY2 are provided and an aspherical lens is inserted separately from the cylindrical lens CY2, an example of which is shown in FIG. 2.
In terms of the characteristic, the f.theta. lens often has a positive distortion. In order to compensate for such distortion and compensate for a high order distortion from positive to negative in a wide angle of view, the aspherical shape is desirably satisfied with the following condition.
.SIGMA..DELTA.Xi(.phi.i)-.SIGMA..DELTA.Xj(.phi.j)>0
where
.DELTA.Xi: displacement of an aspherical surface of a surface S.sub.i on the object side
.DELTA.Xj: displacement of an aspherical surface of a surface S.sub.j on the image side
.phi.i, .phi.j: height from an optical axis at a point where the light at the maximum angle of view intersects the aspherical surface
BRIEF DESCRIPTION OF THE DRAWINGS
FIGS. 1a and 1b is a view of an optical arrangement in a first embodiment of a scanning optical system in accordance with the present invention, and
FIG. 2 is a partial view of an optical arrangement in another embodiment thereof.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
In the following, the effects of the present invention are specifically shown by way of the embodiments.
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Embodiment 1
D
R d.sub.o = 40.0
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1 72.0 5.0 n = 1.51462
2 .infin. 254.6
3 .infin. 5.0 n = 1.51462 Beam
*4 -60.0 302.0 shaping
5 .infin. 5.0 n = 1.51462 system
6 -218.0 110.0
7 .infin. (polygon
70.0
surface)
8 -290.4071 8.5 n = 1.74967
9 -122.5165 217.0
*10 26.5 5.0 n = 1.52065
11 .infin. 53 mm
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*Mark indicates the cylindrical surface.
Diameter of a beam emitted from a laser tube: 0.7 mm
.lambda.=6328 .ANG.
The 11th surface is formed into aspherical surface as follows: ##EQU1## and an aspherical shape are indicated.
Coefficient of aspherical surface
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A.sub.4 = -0.48 .times. 10.sup.-7
A.sub.6 = +0.66 .times. 10.sup.-11
A.sub.8 = -0.584 .times. 10.sup.-15
A.sub.10 = 0.398 .times. 10.sup.-20
A.sub.12 = 0.113 .times. 10.sup.-23
K = 0
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Focal length of the f.theta. lens by the 8th and 9th surfaces: f.sub.1 =276.68 mm
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Rotary Angle of Polygon and Drum Spot Position
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Incident angle
0.0 mm
0.108
0.18 0.252
0.324
0.360
0.390
by polygon
rotation
.theta. sin.theta.
Ideal spot
0.0 mm
29.377
49.134
69.158
89.576
99.977
108.76
position of
drum surface
f = 271.478
Ideal spot
0.0 mm
29.377
49.108
69.180
89.645
99.979
108.78
position of
drum surface
f = 271.478
with aspherical
surface
Ideal spot
0.0 mm
29.453
49.398
69.825
90.967
101.89
111.21
position of
drum surface
f = 271.478
without aspher-
ical surface
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Embodiment 2
D
R d.sub.o = 40.0
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1 72.0 5.0 n = 1.51462
2 .infin. 254.6
3 .infin. 5.0 n = 1.51462 Beam
*4 -60.0 302.0 shaping
5 .infin. 5.0 n = 1.51462 system
6 -218.0 110.0
7 .infin. (polygon
70.0
surface)
8 -380.0 6.0 n = 1.49012
9 -100.46 217.0
*10 25.2 5.0 n = 1.49012
11 .infin. 53.0
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Coefficient of an aspherical surface of the 9th surface:
K=-0.11
Coefficient of an aspherical surface of the 11th surface:
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A.sub.4 = -0.48 .times. 10.sup.-7
P.sub.4 = 4.0
A.sub.6 = 0.66 .times. 10.sup.-11
P.sub.6 = 6.0
A.sub.8 = -0.70 .times. 10.sup.-15
P.sub.8 = 8.0
A.sub.10 = 0.65 .times. 10.sup.-20
P.sub.10 = 10.0
A.sub.12 = 0.165 .times. 10.sup.-23
P.sub.12 = 12.0
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Incidence
0.0 0.108 0.180
0.254
0.324
0.360
0.39
sin .theta.
Spot position
0.0 mm
29.544 mm
49.407
69.60
90.079
100.43
109.44
of drum sur-
face
Ideal 0.0 29.544
49.413
69.55
90.080
100.55
103.38
position
Differential
0.0 0.0 -0.006
+0.05
-0.001
-0.12
+0.06
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With the above-described configuration, in the present invention, it is possible to compensate for the distortion by a very simple construction without special compensating members. Due to the falling compensation, in the optical system in which the cylindrical lens CY2 is inserted, the distortion sometimes occurs due to the CY2 itself. On the other hand, in the present invention, the compensation becomes possible by introducing an aspherical surface into one surface.
While in the above-described embodiment, the focusing lens is employed which has the f.theta. characteristic, it will be noted that the distortion caused by the lens having the sin .theta. characteristic may be compensated for in exactly the same manner.
Furthermore, a description has been made of the embodiment in which a single lens is used as the f.theta. lens. It is known however that if a plurality of lens systems are used to form a wide angle of view, the distortion changes as the angle of view increases from positive to negative due to the high-order aberration. However, it is possible to compensate for the high-order distortion as described by selecting a suitable aspherical shape.
While the optical system including a cylindrical lens has been described as an embodiment, it will be noted that the present invention may be embodied into an optical system having no cylindrical lens and a toroidal lens.
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