Data processing: measuring – calibrating – or testing – Measurement system – Dimensional determination
Reexamination Certificate
1999-05-20
2001-12-11
Grimley, Arthur T. (Department: 2852)
Data processing: measuring, calibrating, or testing
Measurement system
Dimensional determination
C702S150000, C702S153000, C345S158000, C359S206100, C359S662000, C359S708000
Reexamination Certificate
active
06330524
ABSTRACT:
TECHNICAL FIELD
The present invention relates to an fØ lens for use in a scanning optical system.
BACKGROUND TECHNOLOGY
A scanning optical system A for use with a printing unit such as a laser printer, copying machine, facsimile machine and the like has generally a configuration as shown in FIG.
10
.
In
FIG. 10
, reference numeral
1
sets forth an LD unit with a semiconductor laser and the like installed therein, which emits a minutely converged beam light
2
. Reference numeral
3
sets forth a first optical system which converges the beam light
2
only in a sub-scanning direction (in a direction in which a photosensitive drum rotates). Reference numeral
4
sets forth a polygon mirror which assigns the beam light into a main scanning direction upon rotating. Reference numeral
5
sets forth a second optical system composed of an f&thgr; lens, which converges the beam light into the main scanning direction (an axial direction of the photosensitive drum) and the sub-scanning direction to form an electrostatic latent image by the converged imaging on a photosensitive member
6
of the photosensitive drum or the like.
It is to be noted herein that the second optical system
5
is required to have the function of an f&thgr; lens compensation (compensation for linearly maintaining a relationship (X=f&thgr;) of a rotating angle &thgr;/2 of the polygon mirror with a scanning position X of the image formation on the photosensitive drum, in addition to the converging action. At this end, in usual occasions, the second optical system comprises a combination of two or three lenses.
On the other hand, in order to reduce a number of parts and to make the scanning optical system compact in size and light in weight, an f&thgr; lens composed of a single lens is proposed (Japanese Patent Unexamined Publication No. 5-323,223).
This proposed f&thgr; lens is designed so as to have the generating line corresponding to the main scanning direction represented by an aspherical formula as follows:
X
=
Y
2
/
R
1
+
1
-
(
1
+
K
)
(
Y
/
R
)
2
+
B
4
Y
4
+
B
6
Y
6
+
B
8
Y
8
+
B
10
Y
10
where
R is the radius of the curvature; and
K, B
4
, B
6
, B
8
, and B
10
are each an aspherical coefficient;
and to have the meridional line corresponding to the sub-scanning direction represented by the formula representing a toric plane as follows:
S
=
Z
2
/
r
1
+
1
-
(
Z
/
r
′
)
2
Further, the technology as disclosed in the above Japanese patent publication is configured such that a slit-shaped diaphragm extending in the main scanning direction is disposed immediately in front of the f&thgr; lens so as to make the F-number in the sub-scanning direction constant regardless of the beam spot position on the photosensitive member.
When the f&thgr; lens having a single lens configuration composed of the aspherical lens as described above is used, the above patent publication discloses to the effect that the optical performance of the scanning optical system is indicated so as to form a spot having a diameter of 120 &mgr;m or larger on the photosensitive member.
In the f&thgr; lens using the conventional designing formula as described above, the aspherical formula corresponds to the main scanning direction only. The sub-scanning direction is configured by the toric plane of a simple form and is designed so as to make the F-number constant in the combination with the slit-shaped diaphragm. The conventional configuration, however, suffers from the disadvantage that performance necessary for high resolution cannot be achieved for reasons, for instance, due to the difficulty in making the spot size minute. This may cause the problem particularly when the projection magnification should be made larger so as to extend the scanning width L on the photosensitive member to correspond to, e.g., an A3 paper size.
Therefore, the present invention has the object to provide an f&thgr; lens so adapted as to readily make resolution higher by devising an aspherical formula for use in designing, even if it is composed of a single lens and no slit is disposed.
DISCLOSURE OF THE INVENTION
The present invention provides a scanning optical system for reflecting a beam light generated from a light source on a rotating polygon mirror and for scanning the beam light and forming an image on a photosensitive member through an f&thgr; lens for converging the beam light and effecting the f&thgr; compensation, in which the f&thgr; lens is represented by the formula (1) as follows:
Z
=
C
x
X
2
1
+
1
-
(
1
+
K
)
C
x
2
X
2
+
∑
n
=
3
u
A
n
&LeftBracketingBar;
X
n
&RightBracketingBar;
+
C
y
Y
2
(
1
+
∑
m
=
2
w
B
m
&LeftBracketingBar;
X
m
&RightBracketingBar;
)
1
+
1
-
[
1
+
K
y
(
1
+
∑
j
=
1
v
G
j
X
2
j
)
]
[
C
y
2
Y
2
(
1
+
∑
m
=
2
w
B
m
&LeftBracketingBar;
X
m
&RightBracketingBar;
)
2
]
-
C
x
=
1
/
R
x
C
y
=
1
/
R
y
(
1
)
where
Cx, K, An, Cy, Bm, Ky, and Gj are each an optional coefficient; and
u, v, and w are each an integer.
The scanning optical system is further characterized in that the f&thgr; lens is designed in a single-lens configuration by using an optional term containing an odd-numbered degree and an even-numbered degree in each of &Sgr;An|X
n
|, &Sgr; Bm|X
m
| and &Sgr;GjX
2j
in the aspherical formula representing the shape of an incident surface or an outgoing surface of the f&thgr; lens, as represented above.
The above aspherical formula (1) represents the height Z in the light-axial direction of the lens surface with respect to the position X in the main scanning direction and the position Y in the sub-scanning direction. The lens surface of the f&thgr; lens defined by the aspherical formula (1) has a shape extending each along the main scanning direction (the X-axis) and the sub-scanning direction (the Y-axis) formed by a free curve.
The free curve in the main scanning direction is defined by the sum of the first and second terms of the above aspherical formula (1) as follows:
C
x
X
2
1
+
1
-
(
1
+
K
)
C
x
2
X
2
+
∑
n
=
3
u
A
n
&LeftBracketingBar;
X
n
&RightBracketingBar;
C
x
=
1
/
R
x
On the other hand, the free curve in the sub-scanning direction is defined by the third term of the above aspherical formula (1) as follows:
C
y
Y
2
(
1
+
∑
m
=
2
w
B
m
&LeftBracketingBar;
X
m
&RightBracketingBar;
)
1
+
1
-
[
1
+
K
y
(
1
+
∑
j
=
1
v
G
j
X
2
j
)
]
[
C
y
2
(
Y
2
(
1
+
∑
m
=
2
w
B
m
&LeftBracketingBar;
X
m
&RightBracketingBar;
)
)
2
]
C
y
=
1
/
R
y
The first term represents a basic curve represented by a curvature Cx in the X-axial direction (a reciprocal number of a radius Rx) and an eccentricity K. A free curve which changes in the main scanning direction X as indicated in FIG.
4
(
b
) is formed by adding a plurality of n-th curves using X of the second term as a variable to the basic curve.
The third term is a term that changes a curvature Cy in the Y-axial direction (a reciprocal number of a radius Ry), which determines a YZ sectional shape, and an eccentricity Ky in accordance with an X-axial position. In other words, a plurality of m-th functions using X as a variable is added to 1, and the sum as a coefficient is then multiplied by the curvature Cy. Further, the sum obtained by adding the sum of plural (2j)-th functions using X as a variable to 1 is multiplied as a coefficient by the eccentricity Ky.
The free curve extending along the sub-scanning direction Y can be formed into a desired shape as shown in FIG.
4
(
c
) by changing the eccentricity and the curvature in accordance the position X in the main scanning direction by optionally changing the (2j)-th function and the m-th function.
As shown in
FIG. 3
representing the optical path diagram of the scanning optical system of
FIG. 1
, when a beam light generating from the light source is incident to the polygon mirror in the main s
Suzuki Takatoshi
Xing Tingwen
Arent Fox Kintner & Plotkin & Kahn, PLLC
Grimley Arthur T.
Le John
Nippon Aspehrical Lens Co., Ltd.
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