Scanner optics and image formation apparatus using the same

The scanner optics of this invention includes a condensing lens arrangement composed of a first aspherical lens having a positive refractive power and a convex meniscus surface on the side of the scanning surface and a second toric lens of which incident surface is saddle toroidal where a point on the incident surface has a greater radius of curvature in the sub-scanning direction as the point is farther from the optical axis in the scanning direction. A laser light flux emitted from a light source is deflected and scanned by a polygon mirror so as to form an image on a scanning surface via the condensing lens arrangement.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to a scanner optics used for a laser printer 
and the like, and more specifically relates to a scanner optics having a 
function of compensating a tilt of an optical deflection surface of a 
polygon mirror which may occur when a laser light flux is deflected by the 
polygon mirror, and an image formation apparatus using such a scanner 
optics. 
2. Description of the Related Art 
A pre-objective type scanner optics is often used for the conventional 
laser printer and the like, where a condensing lens arrangement is 
disposed after a polygon mirror which deflects a laser light flux. In the 
pre-objective type scanner optics, a laser light flux emitted from a laser 
diode is made substantially parallel by a collimator lens. After the 
beam-shaping by a cylindrical lens and the like, the parallel laser light 
flux is incident to the polygon mirror. The incident light flux is 
reflected and deflected by the polygon mirror, so as to form a spot on a 
scanning surface such as a photosensitive drum via a condensing lens 
arrangement. The polygon mirror is rotated at a constant angular velocity, 
thus realizing the scanning of the surface with the spot. The condensing 
lens arrangement has an optical function of keeping the scanning speed of 
the spot constant in a scanning direction. The condensing lens arrangement 
also has a function of compensating "a tilt of the deflection surface of 
the polygon mirror" (hereinafter, simply referred to as a "surface tilt") 
by arranging the deflection point on the polygon mirror and the scanning 
surface of the photosensitive drum so that they are in the conjugate 
relationship in a sub-scanning direction from the geometrical optics point 
of view. 
A known general method for compensating the surface tilt is to provide the 
condensing lens arrangement with an anamorphic surface, as described in 
Japanese Laid-Open Patent Publication No. 61-243422, for example. The 
"anamorphic surface" as used herein refers to a surface which is toric and 
aspherical. However, a distortion, especially in the sub-scanning 
direction, cannot be sufficiently corrected. As a result, the diameter of 
the spot formed on the scanning surface varies depending on the position 
of the scanning, making it difficult to realize image formation with a 
broad field angle and high resolution. 
In a scanner optics arranged in a two-dimensional plane, the optical 
characteristics such as spherical aberration and distortion are asymmetric 
in the scanning direction, making it difficult to uniformly correct the 
image formation performance over the entire scanning surface. 
The objective of the present invention is to provide a small-size scanner 
optics with a broad field angle and high performance over the entire 
scanning surface. 
SUMMARY OF THE INVENTION 
The scanner optics of this invention deflects a laser light flux emitted 
from a light source with a polygon mirror and scans a scanning surface 
with the deflected laser light flux via a condensing lens arrangement. The 
condensing lens arrangement comprises: a first aspherical lens having a 
positive refractive power and a convex meniscus surface on a side of the 
scanning surface; and a second toric lens having a positive refractive 
power, the refractive power of the second toric lens in a sub-scanning 
direction at a center portion in a scanning direction being different from 
the refractive power of She second toric lens at a peripheral portion. 
In one example, an incident surface of the second toric lens is saddle 
toroidal where a point on the incident surface has a greater radius of 
curvature in the sub-scanning direction as the point is farther from an 
optical axis in the scanning direction. 
In another example, the second toric lens has at least one aspherical 
surface in the scanning direction. 
In still another example, an emergent surface of the second toric lens is 
barrel toroidal where a point on the emergent surface has a smaller radius 
of curvature in the sub-scanning direction as the point is farther from 
the optical axis in the scanning direction. 
In still another example, an expression (1): 
##EQU1## 
is satisfied where r.sub.3x is a radius of curvature of the incident 
surface of the second toric lens in the subscanning direction at a center 
of the optical axis, r.sub.4x is a radius of curvature of the emergent 
surface of the second toric lens in the sub-scanning direction at the 
center of the optical axis, f.sub.y is a synthetic focal length of the 
first aspherical lens and the second toric lens in the scanning direction, 
and d.sub.2 is a thickness of the second toric lens. 
In still another example, an expression (2): 
##EQU2## 
is satisfied where YD is an amount of decentering of the condensing lens 
arrangement in the scanning direction with respect to the optical axis, 
y.sub.m is a maximum image height formed by the condensing lens 
arrangement, and f.sub.y is a synthetic focal length of the first 
aspherical lens and the second toric lens in the scanning direction. 
In another aspect of the present invention, an image formation apparatus is 
provided. The apparatus comprises: means for electrifying a photosensitive 
surface; means for forming a static latent image on the photosensitive 
surface by use of the scanner optics described in claim 1; means for 
developing the static latent image; and means for transferring the 
developed image onto a transfer medium. 
In the scanner optics of the present invention, the incident surface of the 
second toric lens of the condensing lens arrangement is saddle toroidal 
and the emergent surface thereof is barrel toroidal. With this 
configuration, an increase in the amount of distortion in the sub-scanning 
direction caused by expanding the field angle can be effectively 
corrected, and a variation in the diameter of the spot formed on the 
scanning surface depending on the position of the scanning can be 
minimized. 
By decentering the condensing lens arrangement in the scanning direction 
with respect to the optical axis, a good optical performance can be 
obtained over the entire scanning width. 
Thus, the invention described herein makes possible the advantages of (1) 
providing a scanner optics capable of effectively correcting a distortion 
in the sub-scanning direction while realizing a broad field angle and 
minimizing a variation in the diameter of a spot formed on a scanning 
surface, (2) providing a scanner optics capable of achieving a good 
optical performance over the entire scanning width, and (3) providing a 
small-size image formation apparatus with a broad field angle and high 
resolution at low cost. 
These and other advantages of the present invention will become apparent to 
those skilled in the art upon reading and understanding the following 
detailed description with reference to the accompanying figures.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
The present invention will be described by way of examples with reference 
to the accompanying drawings. In the following description, the same 
reference numerals in the drawings denote the same components. 
FIG. 1 shows a configuration of a scanner optics which covers Examples 1, 
2, and 3 of the present invention. The scanner optics includes a laser 
diode 1, a collimator lens 2, a cylindrical lens 3, a polygon mirror 4, a 
first lens 5, and a second lens 6. The polygon mirror 4 rotates around a 
rotational axis 8. The reference numeral 7 denotes a photosensitive drum. 
FIGS. 2 and 3 are sectional views of the scanner optics of Example 1 as is 
viewed in a scanning direction Y and a sub-scanning direction X, 
respectively. FIGS. 6 and 7 are sectional views of the scanner optics. of 
Examples 2 and 3 as is viewed in the scanning direction Y and the 
sub-scanning direction X, respectively. 
Hereinbelow, the operation of the scanner optics will be described with 
reference to FIGS. 1 and 2. The "scanning direction Y" refers to a 
direction of the rotational axis of the photosensitive drum shown in FIG. 
1, while the "sub-scanning direction X" refers to a direction vertical 
both To a direction of a laser light flux incident to the photosensitive 
drum shown in FIG. 1 and the rotational axis of the photosensitive drum. 
Referring to FIGS. 1, 2 and 3, a laser light flux emitted from the laser 
diode 1 is made substantially parallel by the collimator lens 2 and then 
converged by the cylindrical lens 3 so that a laser flux in the 
sub-scanning direction X forms an image in the vicinity of the polygon 
mirror 4. The polygon mirror 4 which rotates around the rotational axis 8 
deflects the incident laser light flux to effect scanning. The deflected 
laser light flux passes through a condensing lens arrangement composed of 
the first lens 5 which is an aspherical lens and the second lens 6 which 
is an toric lens, so as to form an image on the photosensitive drum 7. The 
first lens 5 and the second lens 6 are arranged so that the deflection 
point on the polygon mirror 4 and the scanning surface of the 
photosensitive drum 7 are in a conjugate relationship in the sub-scanning 
direction X from the geometrical optics point of view. Thus, a tilt of the 
polygon mirror 4 is compensated. The incident surface of the toric lens 6 
is saddle toroidal where a point on the incident surface has a greater 
radius of curvature in the sub-scanning direction X as the point is 
farther from the optical axis in the scanning direction Y. This saddle 
toroidal surface is effective in correcting a distortion in the 
sub-scanning direction X. However, when a scanner optics having a broader 
field angle is desired, the saddle toroidal surface is not enough to 
sufficiently correct a distortion in the sub-scanning direction X, and the 
curvature in the sub-scanning direction X also becomes smaller. The 
production of such a scanner optics is difficult, resulting in increasing 
production cost. This problem can be overcome by adopting a barrel 
toroidal surface where a point on the incident surface of the toric lens 6 
has a smaller radius of curvature in the sub-scanning direction X as the 
point is farther from the optical axis in the scanning direction Y. Thus, 
a distortion in the sub-scanning direction X can be effectively corrected 
even when a broader field angle is desired. A variation in the diameter of 
the spot formed on the scanning surface can also be minimized. 
The scanner optics of this embodiment satisfies expression (1): 
##EQU3## 
where r.sub.3x is the radius of curvature of the incident surface of the 
second lens 6 as the toric lens in the sub-scanning direction X at the 
center of the optical axis, r.sub.4x is the radius of curvature of the 
emergent surface of the second lens 6 in the sub-scanning direction X at 
the center of the optical axis, f.sub.y is synthetic focal length of the 
first lens 5 and the second lens 6 constituting the condensing lens 
arrangement in the scanning direction Y, and d.sub.2 is the thickness of 
the second lens 6 as the toric lens. 
Expression (1) will be explained from the technical point of view. 
Expression (1) relates to the ratio of the radius of curvature r.sub.3x of 
the incident surface of the toric lens 6 in the sub-scanning direction X 
at the center of the optical axis, the radius of curvature r.sub.4x of the 
emergent surface of the toric lens 6 in the sub-scanning direction X at the 
center of the optical axis, the synthetic focal length f.sub.y of the 
aspherical lens 5 and the toric lens 6 in the scanning direction Y, and 
the thickness d2 of the toric lens 6. This is mainly used for effectively 
correcting a distortion in the sub-scanning direction X in a broad field 
angle region. When both the radius of curvature r.sub.3x and the radius of 
curvature r.sub.4x are small, and the resultant ratio exceeds the upper 
limit of expression (1), the correction of the distortion in the 
sub-scanning direction x is excessive. As a result, a desired optical 
performance is not obtainable, and thus it is difficult to expand the 
field angle of the scanner optics. Conversely, when both the radius of 
curvature r.sub.3x and the radius of curvature r.sub.4x are large, and the 
resultant ratio exceeds the lower limit of expression (1), the correction 
of the distortion in the sub-scanning direction X is insufficient. 
In this embodiment, in order to effectively correct a distortion in the 
scanning direction Y and the f8 characteristic and obtain a good optical 
performance over the entire effective scanning width, the toric lens 6 
preferably has at least one aspherical surface in the scanning direction 
Y. 
The scanner optics of this embodiment also satisfies expression (2): 
##EQU4## 
where YD is the amount of decentering of the first lens 5 and the second 
lens 6 constituting the condensing lens arrangement in the scanning 
direction Y with respect to the optical axis thereof, y.sub.m is the 
maximum image height formed by the first lens 5 and the second lens 6, and 
f.sub.y is the synthetic focal length of the first lens 5 and the second 
lens 6 in the scanning direction Y. 
Expression (2) will be explained from the technical point of view. 
Expression (2) relates to the ratio of the amount of decentering YD of the 
first lens 5 and the second lens 6 in the scanning direction Y with 
respect to the optical axis, the synthetic focal length f.sub.y of the 
first lens 5 and the second lens 6 in the scanning direction Y, and the 
maximum image height y.sub.m formed by the first lens 5 and the second 
lens 6. This is mainly used for the condensing lens arrangement 
constructed in the two-dimensional plane, so as to prevent the optical 
performance of the scanner optics from degrading due to the asymmetry of 
the image formation performance such as spherical aberration and 
distortion in the scanning direction Y, and thus to obtain a good optical 
performance over the entire effective scanning width. When the amount of 
decentering YD is small, and the resultant ratio exceeds the upper limit 
of expression (2), the correction of the asymmetry of the image formation 
performance in the scanning direction Y is insufficient. Thus, it is 
difficult to effectively correct the optical performance. On The contrary, 
when the amount of decentering YD is great, and The resultant ratio exceeds 
the lower limit of expression (2), the optical performance degrades in a 
direction reverse to the direction of the image height of which correction 
is insufficient in the scanning direction Y. 
As described above, by adopting the lens configuration and conditions 
according to the present invention, a small-size scanner optics with a 
broad field angle can be realized. Using such a scanner optics, a 
distortion in the scanning direction Y and the sub-scanning direction X 
can be effectively corrected, and a good optical performance can be 
obtained over the entire scanning width. 
Exemplary parameters are shown below as Examples 1 to 3. The exemplary 
parameters of Example 2 satisfy expression (1) and the exemplary 
parameters of Example 3 satisfy expressions (1) and (2). In the examples, 
f.sub.y is the synthetic focal length of The first lens 5 and the second 
lens 6 in the scanning direction Y, F denotes an F number, and .theta. 
denotes the scanning angle. r.sub.1, r.sub.2, and r.sub.4 ; are paraxial 
radii of curvatures of the lens surfaces of the condensing lens 
arrangement (the. order corresponds to the actual order from the 
deflection point side. This is also applicable to The following 
description): r.sub.3y and r.sub.4y are paraxial radii of curvatures of 
the lens surfaces in the scanning direction Y: r.sub.3x and r.sub.4x are 
radii of curvatures of the lens surfaces in the sub-scanning direction X 
at the center of the optical axis: d.sub.1, d.sub.2, d.sub.3, and d.sub.4 
are distances between the adjacent lens surfaces, i.e., the surface 
separation or the air gap: and n.sub.1 and n.sub.2 are refractive indexes 
of lens materials at a wavelength of 780 nm. The amount of decentering of 
the first lens 5 and the second lens 6 constituting The condensing lens 
arrangement with respect to the optical axis in the scanning direction Y 
is YD, and the aspherical surfaces (indicated by * mark) are defined by 
expression (3): 
##EQU5## 
where Z is the distance of a vertex of an aspherical surface of which 
height from the optical axis is y from the nodal plane, y is the height 
from the optical axis, c is the curvature of the aspherical vertex, k is 
the conical constant, and D, E, F, and G are the aspherical coefficients. 
______________________________________ 
(Example 1) 
______________________________________ 
f.sub.y = 175 mm 
.theta. = 18.0.degree. 
F: scanning direction 
37.5 
sub-scanning direction 
37.5 
d.sub.1 = 19.6 
r.sub.1 * = -77.4 
d.sub.2 = 10.0 n.sub.1 = 1.51 
r.sub.2 * = -43.1 
d.sub.3 = 118.2 
r.sub.3y = -421.6 
d.sub.4 = 6.0 n.sub.2 = 1.52 
r.sub.3x = 24.2 
r.sub.4 * = -487.5 
______________________________________ 
The surfaces marked * are aspherical surfaces. The aspherical coefficients 
of these aspherical surfaces are shown below. 
______________________________________ 
r.sub.1 r.sub.2 r.sub.4 
______________________________________ 
k -4.82805 -0.46423 0.0 
D 1.03575 .times. 10.sup.-06 
7.38887 - 10.sup.-07 
-1.50743 .times. 10.sup.-07 
E 1.23933 .times. 10.sup.-09 
4.24684 .times. 10.sup.-10 
6.33546 .times. 10.sup.-12 
F -1.97891 .times. 10.sup.-12 
1.39509 .times. 10.sup.-12 
-4.91801 .times. 10.sup.-16 
G -2.51182 .times. 10.sup.-15 
-1.85545 .times. 10.sup.-12 
1.57302 .times. 10.sup.-20 
______________________________________ 
The amount of distortion and the f.theta. characteristic obtained in 
Example 1 are shown in FIGS. 4 and 5, respectively. 
______________________________________ 
(Example 2) 
______________________________________ 
f.sub.y = 146 mm 
.theta. = 21.6.degree. 
F: scanning direction 
37.5 
YD = 0.0 mm sub-scanning direction 
37.5 
d.sub.1 = 23.1 
r.sub.1 * = -104.6 
d.sub.2 = 13.0 n.sub.1 = 1.51 
r.sub.2 * = -45.0 
d.sub.3 = 96.2 
r.sub.3y = -528.3 
d.sub.4 = 18.0 n.sub.2 = 1.52 
r.sub.3x = 21.8 
r.sub.4y * = -495.0 
r.sub.4x = -240.8 
______________________________________ 
The surfaces marked * are aspherical surfaces. The aspherical coefficients 
of these aspherical surfaces are shown below. 
______________________________________ 
r.sub.1 r.sub.2 r.sub.4y 
______________________________________ 
k -1.51526 -0.20170 0.0 
D 2.16455 .times. 10.sup.-07 
1.17389 .times. 10.sup.-07 
-1.66129 .times. 10.sup.-07 
E -1.30064 .times. 10.sup.-09 
-4.21083 .times. 10.sup.-10 
3.19423 .times. 10.sup.-12 
F -7.11922 .times. 10.sup.-13 
-2.71728 .times. 10.sup.-13 
2.94542 .times. 10.sup.-16 
G 6.68585 .times. 10.sup.-16 
-5.67109 .times. 10.sup.-16 
-2.83341 .times. 10.sup.-20 
______________________________________ 
The amount of distortion and the f.theta. characteristic obtained in 
Example 2 are shown in FIGS. 8 and 9, respectively. 
______________________________________ 
(Example 3) 
______________________________________ 
Y.sub.m = 
108 mm 
f.sub.y = 
145 mm 
.theta. = 
21.7.degree. 
F: scanning direction 
37.5 
YD = 0.3 mm sub-scanning direction 
37.5 
d.sub.1 = 23.0 
r.sub.1 * = 
-104.1 d.sub.2 = 12.9 
n.sub.1 = 1.51 
r.sub.2 * = 
-44.8 d.sub.3 = 95.7 
r.sub.3y = 
-525.8 d.sub.4 = 17.9 
n.sub.2 = 1.52 
r.sub.3x = 
21.7 
r.sub.4y * = 
-492.6 
r.sub.4x = 
-239.6 
______________________________________ 
The surfaces marked * are aspherical surfaces. The aspherical coefficients 
of these aspherical surfaces. are shown below. 
______________________________________ 
r.sub.1 r.sub.2 r.sub.4y 
______________________________________ 
k -1.51526 -2.01696 0.0 
D 4.58412 .times. 10.sup.-07 
1.48629 .times. 10.sup.-07 
-1.66216 .times. 10.sup.-07 
E -1.40979 .times. 10.sup.-09 
-2.29345 .times. 10.sup.-10 
3.07831 .times. 10.sup.-12 
F -1.10948 .times. 10.sup.-12 
-2.96234 .times. 10.sup.-13 
2.45722 .times. 10.sup.-16 
G 8.51806 .times. 10.sup.-16 
-7.96030 .times. 10.sup.-16 
-2.33873 .times. 10.sup.-20 
______________________________________ 
The amount of distortion and the f.theta. characteristic obtained in 
Example 3 are shown in FIGS. 10 and 11, respectively. 
FIG. 12 shows an image formation apparatus adopting the scanner optics of 
the embodiment according to the present invention. 
Referring to FIG. 12, the image formation apparatus includes a 
photosensitive drum 11, a primary electrifier 12, a scanner optics 13 
according to the present invention, a developer 14, a transfer electrifier 
15, a cleaner 16, a sheet feed cassette 17, a sheet feed roller 18, a 
transfer sheet 19, a fixing device 20, a sheet ejection roller 21, and a 
sheet ejection tray 22. 
The operation of the image formation apparatus with the above structure 
will be described. The surface of the photosensitive drum 11 is uniformly 
electrified to have a predetermined polarity by the primary electrifier 
12. Image information is projected onto the electrified surface of the 
photosensitive drum 11 via the. scanner optics 13. Charges on portions of 
the photosensitive drum 11 which are irradiated with light are repelled, 
while charges on the remaining portions which are not irradiated with 
light are maintained, thereby forming a static latent image corresponding 
to the image information. Electrified colored fine grains called toner are 
fed from the developer 14 to the static latent image and attach to the 
remaining charges, so as to develop the image. The developed image is 
superimposed on a transfer sheet 19 fed from the sheet feed cassette 17 
via the sheet feed roller 18. Then, the transfer electrifier 15 applies 
charges having a polarity reverse to that of the toner grains to the outer 
surface of the transfer sheet 19 which is not in contact with the developed 
image. Thus, the image is transferred to the transfer sheet 19. After the 
transfer sheet 19 is separated from the photosensitive drum 11, the 
transferred image on the transfer sheet 19 is fixed by the fixing device 
20. The transfer sheet 19 having the fixed image is then ejected onto the 
sheet ejection tray 22 via the sheet ejection roller 21. Thereafter, the 
photosensitive drum 11 is cleaned by removing the remaining toner by the 
cleaner 16 and returns to the initial electrifying step. 
Thus, a small-size image formation apparatus with a broad field angle and 
high resolution can be realized at low cost by adopting the scanner optics 
of the present invention. 
Various other modifications will be apparent to and can be readily made by 
those skilled in the art without departing from the scope and spirit of 
this invention. Accordingly, it is not intended that the. scope of the 
claims appended hereto be limited to the description as set forth herein, 
but rather that the claims be broadly construed.