U.S. patent application number 09/745079 was filed with the patent office on 2001-08-23 for optical imaging system.
Invention is credited to Kittaka, Shigeo.
Application Number | 20010015853 09/745079 |
Document ID | / |
Family ID | 18474953 |
Filed Date | 2001-08-23 |
United States Patent
Application |
20010015853 |
Kind Code |
A1 |
Kittaka, Shigeo |
August 23, 2001 |
Optical imaging system
Abstract
A high performance optical imaging system can be provided by
minimizing the overlapping degree m, increasing the quantity of
light of the rod lens array and improving the resolving power while
taking into account the irregularity of the quantity of light when
a dislocation between a sensor and an optical axis of an entire rod
lens array occurs. In the optical imaging system, a plurality of
rod lenses with a refractive index distribution in the radial
direction are arranged in two rows in a rod lens array with their
optical axes in parallel to each other. This optical imaging system
focuses light from a manuscript plane onto an image plane, the
planes being arranged on the two sides of the rod lens array. The
overlapping degree m defined as the following equation (Eq. 10) is
in a range of 0.91.ltoreq.m.ltoreq.1.01; m=X.sub.0/2R (Eq. 10)
wherein X.sub.0 denotes an image radius that the rod lenses project
onto the image plane and 2R denotes a distance between the optical
axes of neighboring rod lenses.
Inventors: |
Kittaka, Shigeo; (Osaka,
JP) |
Correspondence
Address: |
MERCHANT & GOULD
P O BOX 2903
MINNEAPOLIS
MN
55402-0903
US
|
Family ID: |
18474953 |
Appl. No.: |
09/745079 |
Filed: |
December 20, 2000 |
Current U.S.
Class: |
359/623 ;
359/619; 359/621; 359/622 |
Current CPC
Class: |
G02B 3/0087 20130101;
G02B 3/0037 20130101; H04N 1/0312 20130101; H04N 1/0311
20130101 |
Class at
Publication: |
359/623 ;
359/622; 359/621; 359/619 |
International
Class: |
G02B 027/10 |
Foreign Application Data
Date |
Code |
Application Number |
Dec 20, 1999 |
JP |
11-361813 |
Claims
What is claimed is:
1. An optical imaging system for focusing light from a manuscript
plane onto an image plane, comprising: a rod lens array having a
plurality of rod lenses with a refractive index distribution in a
radial direction that are arranged in two rows so that their
optical axes are in parallel to each other; wherein an overlapping
degree m expressed by the following equation (Eq. 1) is in a range
of 0.91.ltoreq.m.ltoreq.1.01; m=X.sub.0/2R (Eq. 1) wherein 2 R
denotes a distance between the optical axes of neighboring rod
lenses and X.sub.0 denotes an image radius that the rod lenses
project onto the image plane.
2. The optical imaging system according to claim 1, wherein the
overlapping degree m is in the range of
0.93.ltoreq.m.ltoreq.0.97.
3. The optical imaging system according to claim 1, wherein R is in
the range of 0.05 mm.ltoreq.R.ltoreq.0.60 mm.
4. The optical imaging system according to claim 1, wherein a
radius r.sub.0 of a portion functioning as a lens of the rod lenses
is in the range of 0.50 R.ltoreq.r.sub.0.ltoreq.1.0 R.
5. The optical imaging system according to claim 1, wherein a
shading mask having an approximately rectangular shaped opening
portion opening along the longitudinal direction of the rod lens
array is arranged on at least one side of the rod lens array.
6. The optical imaging system according to claim 5, wherein the
opening portion of the shading mask is symmetric to the central
axis in the longitudinal direction of the lens surface of the rod
lens array.
7. The optical imaging system according to claim 6, wherein a half
width W of the opening portion of the shading mask is in the range
of ({square root}{fraction (3/2)}) R+0.1
r.sub.0.ltoreq.W.ltoreq.({square root}{fraction (3/2)}) R+0.6
r.sub.0, wherein r.sub.0 denotes a radius of a portion functioning
as a lens of the rod lenses.
8. The optical imaging system according to claim 1, wherein the
refractive index distribution of the rod lenses is expressed by the
following equation (Eq. 2); n(r).sup.2=n.sub.0.sup.2.cndot.{1-
(g.cndot.r).sup.2+h.sub.4.cndot.(g.cndot.r).sup.4h.sub.6.cndot.(g.cndot.r-
).sup. 6+h.sub.8.cndot.(g.cndot.r).sup.8+. . . } (Eq. 2) wherein r
denotes a radial distance from an optical axis of the rod lenses,
n.sub.0 denotes a refractive index at the optical axis of the rod
lenses, and g, h.sub.4, h.sub.6 and h.sub.8 denote coefficients of
the refractive index distribution.
9. The optical imaging system according to claim 8, wherein the
refractive index n.sub.0 at the optical axis of the rod lenses is
in the range of 1.4.ltoreq. n.sub.0.ltoreq.1.8.
10. The optical imaging system according to claim 8, wherein a
product n.sub.0.cndot.g.cndot.r.sub.0 is in the range of
0.05.ltoreq.n.sub.0.cndo- t.g.cndot.r.sub.0.ltoreq.0.50, wherein
r.sub.0 denotes a radius of a portion functioning as a lens of the
rod lenses.
11. The optical imaging system according to claim 8, wherein
Z.sub.0/P is in the range of 0.5<Z.sub.0/P<1.0, wherein
Z.sub.0 denotes a length of the rod lens and P=2.pi./g denotes a
one-pitch length of the rod lenses.
12. The optical imaging system according to claim 1, wherein a
parallel plane transparent substrate is arranged so that the
manuscript plane is positioned at a front focal position of the rod
lens array.
13. The optical imaging system according to claim 12, wherein the
parallel plane transparent substrate is in contact with the lens
surface of the rod lens array.
Description
FIELD OF THE INVENTION
[0001] The present invention relates to an optical imaging system
used in an image transmission portion of an optical device, for
example, a facsimile device, a copier, a printer, a scanner, or the
like. More particularly, the present invention relates to an
optical imaging system including a rod lens array, in which a
plurality of rod lenses are arranged in an array.
BACKGROUND OF THE INVENTION
[0002] In an optical device, for example, a facsimile device, a
copier, a printer, a scanner, or the like, to read out information
on a manuscript plane by converting the information into an
electrical signal, various kinds of scanning devices are used. One
form of the scanning device is a contact type device. This contact
type scanning device is formed by incorporating various parts
including a lightening system, a rod lens array that is a
one-to-one imaging device, a sensor, a cover glass (a transparent
substrate), and the like, into one frame. In general, a manuscript
is brought into contact with the surface of the cover glass and
illuminated by the lighting system. The illuminated manuscript is
imaged on the censor by the rod lens array and converted into an
electric signal. Herein, the rod lens array is a one-to-one optical
imaging system in which a plurality of rod lenses having a
refractive index distribution in a radial direction are arranged in
one row or two rows (see FIG. 2).
[0003] An example of a lens material used for a rod lens array
includes glass, synthetic resin, or the like. A glass lens having a
refractive index distribution is produced, for example, by an ion
exchange method.
[0004] A single rod lens forms a one-to-one image within the range
of a circle having a radius X.sub.0 (field of view). The quantity
of light is at the maximum on the optical axis and decreases with
greater distance from the optical axis. Therefore, the distribution
of the quantity of light in the longitudinal direction of a rod
lens array has irregularity with the period corresponding to the
distance between lenses. The magnitude of the irregularity of the
quantity of light is defined as: 100 {(maximum quantity of
light)-(minimum quantity of light)} /(minimum quantity of light) %,
and determined by the overlapping degree m expressed by the
following equation (Eq. 3):
m=X.sub.0/2R (Eq. 3)
[0005] wherein 2 R denotes the distance between the optical axes of
neighboring rod lenses.
[0006] FIG. 15 shows a relationship between the overlapping degree
m and the irregularity of the quantity of light, which are
calculated by the below mentioned equation of the distribution of
the quantity of light (Eq. 9), in a rod lens array in which a
plurality of rod lenses are arranged in two rows. FIG. 15 shows the
case of so-called "linear scanning method" using a very narrow
range of light on the central axis of the image plane (see FIG. 2).
As shown in FIG. 15, the irregularity of the quantity of light
tends to decrease as the overlapping degree m is increased.
However, the irregularity does not decrease monotonically. For
example, at the points of m=0.91, 1.13, 1.37, 1.61, 1.85 . . . ,
the irregularity of the quantity of light takes on local minimum
values. Since the irregularity of the quantity of light on the
sensor should be as small as possible, when it is necessary
particularly to minimize the irregularity of the quantity of light,
the rod lens array is designed so that the overlapping degree m is
approximate to the above-mentioned values. However, the
irregularity of the quantity of light shown in FIG. 15 is the value
when the sensor is arranged exactly on the central axis of the
image plane. Therefore, in actual mass-produced scanning devices,
it is inevitable that a dislocation between the sensor and the
optical axis of an entire rod lens array occurs to some extent due
to errors in dimensions of components or errors in assembling
components. The dislocation of the sensor is defined as .DELTA.X in
FIG. 9. Accordingly, it is suggested that the device is designed so
that the overlapping degree m is shifted somewhat from the
above-mentioned local minimum values, in order to allow the
irregularity of the quantity of light to fall within the range of
not more than a certain level even if the dislocation of the sensor
occurs to some extent (JP 11(1999)-14803A, JP11(1999)-64605A).
[0007] In general, even in the case of a rod lens array using rod
lenses having the same optical characteristics, as the overlapping
degree m becomes smaller, the brightness of the image plane is
enhanced, and the resolution power is increased. FIG. 16 shows the
relationship between the overlapping degree m and average
brightness (in the case of a linear scanning) in a rod lens array
in which a plurality of the same rod lenses are arranged in one row
and in two rows. In FIG. 16, the brightness of the rod lens array
is defined to be 100 when the overlapping degree m is 1.50 and the
rod lenses are arranged in two rows in the rod lens array.
[0008] However, as the overlapping degree m is smaller, the
irregularity of the quantity of light is increased. Thus, in a
practical rod lens array, the overlapping degree m is 1.3 or more
in the case of a rod lens array in which the rod lenses are
arranged in two rows. For example, the lower limit of the
overlapping degree m is set to be 1.36 in the rod lens array in
which the rod lenses are arranged in two rows by Nippon Sheet Glass
Co., Ltd. According to a disclosure of JP11(1999)-14803A, the
desirable overlapping degree m is set to be in the range of
1.46.ltoreq.m.ltoreq.1.64.
[0009] Recently, to provide high speed for a facsimile device, a
scanner, or the like, a brighter rod lens array has been
demanded.
SUMMARY OF THE INVENTION
[0010] It is an object of the present invention to provide a high
performance optical imaging system by minimizing the overlapping
degree m, increasing the quantity of light of the rod lens array
and improving the resolving power while taking into account the
irregularity of the quantity of light when a dislocation between a
sensor and an optical axis of an entire rod lens array occurs.
[0011] In order to achieve the above-mentioned object, the
configuration of the optical imaging system for focusing light from
a manuscript plane onto an image plane according to the present
invention includes a rod lens array having a plurality of rod
lenses with a refractive index distribution in a radial direction
that are arranged in two rows so that their optical axes are in
parallel to each other. An overlapping degree m expressed by the
following equation (Eq. 4) is in a range of
0.91.ltoreq.m.ltoreq.1.01;
m=X.sub.0/2R (Eq. 4)
[0012] wherein 2 R denotes a distance between the optical axes of
neighboring rod lenses and X.sub.0 denotes an image radius that the
rod lenses project onto the image plane.
[0013] According to such a configuration of the optical imaging
system, it is possible to obtain a high performance optical imaging
system in which a quantity of light is increased and the resolution
power is improved.
[0014] Furthermore, in the configuration of the optical imaging
system of the present invention, it is preferable that the
overlapping degree m is in the range of
0.93.ltoreq.m.ltoreq.0.97.
[0015] Furthermore, in the configuration of the optical imaging
system of the present invention, it is preferable that R is in the
range of 0.05mm.ltoreq.R.ltoreq. 0.60 mm. When R is less than 0.05
mm, production of the rod lens array becomes difficult from the
practical viewpoint (for example, handling becomes extremely
difficult). When R is more than 0.60 mm, the entire rod lens array
becomes large, it is difficult to downsize the entire optical
imaging system.
[0016] Furthermore, in the configuration of the optical imaging
system of the present invention, it is preferable that a radius
r.sub.0 of a portion functioning as a lens of the rod lenses is in
the range of 0.50 R.ltoreq.r.sub.0.ltoreq.1.0 R. When r.sub.0 is
less than 0.50 R, the brightness of the image is remarkably
reduced. Therefore, it is needless to say that the maximum r.sub.0
is equal to R.
[0017] Furthermore, in the configuration of the optical imaging
system of the present invention, it is preferable that a shading
mask having an approximately rectangular shaped opening portion
opening along the longitudinal direction of the rod lens array is
arranged on at least one side of the rod lens array. According to
such a preferable configuration, it is possible to reduce the
irregularity of the quantity of light. Furthermore, in this case,
it is preferable that the opening portion of the shading mask is
symmetric to the central axis in the longitudinal direction of the
lens surface of the rod lens array. Furthermore, it is preferable
that a half width W of the opening portion of the shading mask is
in the range of ({square root}{fraction (3/2)})R+0.1
r.sub.0.ltoreq.W.ltoreq.({square root}{fraction (3/2)}) R+0.6
r.sub.0, wherein r.sub.0 denotes a radius of a portion functioning
as a lens of the rod lenses. When the half width W of the opening
portion of the shading mask is less than ({square root}{fraction
(3/2)}) R+0.1 r.sub.0, the quantity of light is much lowered. When
the half width W is more than ({square root}{fraction (3/2)}) R+0.6
r.sub.0, no significant improvement of the irregularity of the
quantity of light is realized.
[0018] Furthermore, in the configuration of the optical imaging
system of the present invention, it is preferable that the
refractive index distribution of the rod lenses is expressed by the
following equation (Eq. 5);
n(r).sup.2=n.sub.0.sup.2.cndot.{1-(g.cndot.r).sup.2+h.sub.4.cndot.(g.cndot-
.r).sup.4+h.sub.6.cndot.(g.cndot.r).sup.6+h.sub.8.cndot.(g.cndot.r).sup.8+-
. . . } (Eq. 5)
[0019] wherein r denotes a radial distance from an optical axis of
the rod lenses, n.sub.0 denotes a refractive index at the optical
axis of the rod lenses, and g, h.sub.4, h.sub.6 and h8 denote
coefficients of the refractive index distribution. Furthermore, in
this case, it is preferable that the refractive index n.sub.0 at
the optical axis of the rod lenses is in the range of
1.4.ltoreq.n.sub.0.ltoreq.1.8. Furthermore, in this case, it is
preferable that a product n.sub.0.cndot.g.cndot.r.sub- .0 is in the
range of 0.05.ltoreq.n.sub.0.cndot.g.cndot.r.sub.0.ltoreq. 0.50,
wherein r.sub.0 denotes a radius of a portion functioning as a lens
of the rod lenses. According to such a preferable configuration, it
is easy to produce rod lenses. Furthermore, in this case, it is
preferable that Z.sub.0/P is in the range of 0.5<Z.sub.0/
P<1.0, wherein Z.sub.0 denotes a length of the rod lens and
P=2.pi./g denotes a one-pitch length of the rod lenses. According
to such a preferable configuration, an erected image can be
obtained.
[0020] Furthermore, in the configuration of the optical imaging
system of the present invention, it is preferable that a parallel
plane transparent substrate is arranged so that the manuscript
plane is positioned at a front focal position of the rod lens
array. According to such a preferable configuration, the manuscript
plane can be set at the front focal position just by pressing the
manuscript to the surface of the transparent substrate. In this
case, it is preferable that the parallel plane transparent
substrate is in contact with the lens surface of the rod lens
array. This easily can be realized by adjusting the thickness of
the transparent substrate. According to such a preferable
configuration, the adjustment of the distance between the rod lens
array and the front focal position can be simplified, which makes
the assembly of the optical imaging system cheaper.
BRIEF DESCRIPTION OF THE DRAWINGS
[0021] FIG. 1 is a perspective view showing a rod lens used in an
optical imaging system according to the present invention.
[0022] FIG. 2 is a perspective view showing an optical imaging
system according to the present invention.
[0023] FIG. 3 is a graph showing a refractive index distribution
curve of the rod lenses used in the optical imaging system
according to the present invention.
[0024] FIG. 4 is a schematic drawing to illustrate the
image-formation with a rod lens used in the optical imaging system
according the present invention.
[0025] FIG. 5 is a schematic drawing of an image composition by a
plurality of rod lenses used in the optical imaging system
according to the present invention.
[0026] FIG. 6 is a graph showing a relationship between an
irregularity of the quantity of light and an overlapping degree
when a dislocation between a sensor and an optical axis of an
entire rod lens array occurs in the optical imaging system
according to the present invention.
[0027] FIG. 7 is a cross sectional view showing an optical imaging
system provided with a parallel plane transparent substrate.
[0028] FIG. 8 is a graph showing a relationships between an
irregularity of the quantity of light and a dislocation between a
sensor and an optical axis of an entire rod lens array in various
Examples 1 to 5 according to the present invention.
[0029] FIG. 9 is a diagram to explain the amount of a dislocation
.DELTA.X of a sensor in the optical imaging system according to the
present invention.
[0030] FIG. 10 is a plan view showing a rod lens array in a second
embodiment according to the present invention.
[0031] FIG. 11 is a graph showing an irregularity of the quantity
of light in Examples 6 and 7 and Comparative Example 3 in the
second embodiment according to the present invention (in the case
where no dislocation occurs).
[0032] FIG. 12 is a graph showing an irregularity of the quantity
of light in Examples 6 and 7 and Comparative Example 3 in the
second embodiment according to the present invention (in the case
where dislocation occurs).
[0033] FIG. 13 is a graph showing an irregularity of the quantity
of light in Examples 8 and 9 and Comparative Example 3 in the
second embodiment according to the present invention (in the case
where no dislocation occurs).
[0034] FIG. 14 is a graph showing an irregularity of the quantity
of light in Examples 8 and 9 and Comparative Example 3 in the
second embodiment according to the present invention (in the case
where dislocation occurs).
[0035] FIG. 15 is a graph showing a relationship between the
overlapping degree m and the irregularity of the quantity of light
amount in a rod lens array in which rod lenses are arranged in two
rows.
[0036] FIG. 16 is a graph showing a relationship between the
overlapping degree m and the brightness in a rod lens array.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0037] The following is a more detailed description of the
embodiments of the present invention.
[0038] (First Embodiment)
[0039] In this embodiment, as is shown in FIGS. 1 and 2, a
plurality of columnar rod lenses 1 with a refractive index
distribution in the radial direction are arranged in two rows in a
rod lens array 2 for one-to-one imaging with their optical axes la
in parallel to each other. This optical imaging system focuses
light from a manuscript plane 3 onto an image plane 4, the planes
being arranged on the two sides of the rod lens array 2.
[0040] As is shown in FIG. 3, the refractive index n of the rod
lenses 1 has a distribution in the radial direction. The refractive
index distribution is expressed by the following equation (Eq.
6);
n(r).sup.2=n.sub.0.sup.2.cndot.{1-(g.cndot.r).sup.2+h.sub.4.cndot.(g.cndot-
.r).sup.4+h.sub.6.cndot.(g.cndot.r).sup.6+h.sub.8.cndot.(g.cndot.r).sup.8+-
. . . } (Eq. 6)
[0041] wherein r is a radial distance from an optical axis 1a of
the rod lenses 1, n(r) is the refractive index at the radial
distance r from the optical axis 1a of the rod lens 1, n.sub.0 is
the refractive index at the optical axis 1a of the rod lenses 1
(central refractive index), and g, h.sub.4, h.sub.6 and h.sub.8 are
coefficients of the refractive index distribution.
[0042] To attain erected images as shown in FIG. 4, the ratio
Z.sub.0/P has to be in the range of 0.5.ltoreq.Z.sub.0/P<1.0,
wherein Z.sub.0 denotes a length of the rod lenses 1 and P=2 .pi./g
denotes a one-pitch length of the rod lenses 1.
[0043] The distance L.sub.0 between the edge (lens surface) of the
rod lens array 2 and the manuscript plane 3 and the distance
L.sub.0 between the edge (lens surface) of the rod lens array 2 and
the image plane 4 (see FIG. 2) are expressed by the following
equation (Eq. 7);
L.sub.0=-{1/(n.sub.0.cndot.g)}.cndot.tan (Z.sub.0 .pi./P) . (Eq.
7)
[0044] It is desirable that R is in a range of 0.05
mm.ltoreq.R.ltoreq.0.60 mm, wherein 2 R denotes the distance
between the optical axes of neighboring rod lenses 1.
[0045] Furthermore, it is desirable that the radius r.sub.0 of the
effective lens portion of the rod lenses 1, that is, the radius
r.sub.0 of the portion functioning as a lens, is in a range of 0.50
R.ltoreq.r.sub.0.ltoreq.1.0 R.
[0046] When the neighboring rod lenses 1 are in contact with each
other and the radius r.sub.0 of the portion functioning as a lens
is equal to the radius of the lens, r.sub.0 is equal to R. However,
due to the assembly process of the rod lens array, rod lenses 1 are
arranged somewhat separated from each other, or in order to shade
at the periphery portion of the rod lenses 1 having a bad
refractive index distribution, the periphery portion of the rod
lenses 1 are made to be opaque. In this case, r.sub.0 is not equal
to R.
[0047] When R is less than 0.05 mm, production of the rod lens
array 2 becomes difficult from the practical viewpoint (for
example, handling becomes extremely difficult). When R is more than
0.60 mm, the entire rod lens array 2 becomes large, it is difficult
to downsize the entire optical imaging system.
[0048] Furthermore, when r.sub.0 is less than 0.50 R, the
brightness of the image is remarkably reduced. Therefore, it is
needless to say that the maximum r.sub.0 is equal to R.
[0049] The brightness of the rod lenses 1 depends on the aperture
angle .theta.= n.sub.0.cndot.g.cndot.r.sub.0 (rad), which is an
angle indicating the range over which the lenses can accept light.
As the aperture angle .theta. is larger, a brighter image can be
obtained.
[0050] In order to use the rod lenses 1 for the one-to-one optical
imaging system, it is desirable that the aperture angle .theta. is
0.05 or more. Furthermore, the rod lenses 1 having the aperture
angle .theta. of more than 0.05 are difficult to produce, since the
content of the component (for example, T1.sub.2O, Li.sub.2O, etc.
for glass lens) for forming the refractive index distribution is
limited. Therefore, it is desirable that the aperture angle
.theta.=n.sub.0.cndot.g.cndot.r.sub.0 is in the range of
0.05.ltoreq.n.sub.0.cndot.g.cndot.r.sub.0.ltoreq.0.50.
[0051] It is desirable that the refractive index n.sub.0 at the
optical axis 1a of the rod lenses 1 (central refractive index) is
large because the aperture angle .theta. is increased when the
refractive index n.sub.0 is larger. For example, in the case of a
glass lens, a large amount of univalent cationic components is
contained, the realizable value of n.sub.0 is in the range of
1.4.ltoreq.n.sub.0.ltoreq.1.8.
[0052] In an optical imaging system provided with such a rod lens
array 2, a compound image is formed by a plurality of rod lenses 1
on the image plane 4, as is shown in FIG. 5, so that it is
convenient to introduce a dimensionless factor describing the
amount of overlap, that is, the so-called "overlapping degree".
This overlapping degree m is expressed by the following equation
(Eq. 8):
m=X.sub.0/2R (Eq. 8)
[0053] wherein X.sub.0 is the image radius (field of view) that a
single rod lens 1 projects onto the image plane 4 and is defined as
X.sub.0=-r.sub.0/cos (Z.sub.0 .pi./P).
[0054] FIG. 6 shows the relationship between the overlapping degree
m and the irregularity of the quantity of light when the
overlapping degree m is varied in the range of 0.90 to 1.20.
[0055] The irregularity of the quantity of light when a dislocation
between a sensor and an optical axis of an entire rod lens array 2
occurs can be calculated by the use of the following equation (Eq.
9) representing the distribution of the quantity of light in the
image radius (field of view) X.sub.0:
E(X)=E.sub.0.cndot.{1-(X/X.sub.0).sup.2}.sup.0.5 (Eq. 9)
[0056] wherein E.sub.0 denotes a quantity of light on the optical
axis, X denotes a distance from the optical axis, and E(X) denotes
a quantity of light when the distance from the optical axis is
X.
[0057] As shown in FIG. 6, for example, when m is 1.13, the
irregularity of the quantity of light is minimized on the central
axis (reference 6 in FIG. 9). However, when the dislocation between
the sensor and the optical axis of the entire rod lens array 2
occurs, the irregularity of the quantity of light is increased
rapidly. On the other hand, when m is 0.94, the irregularity of the
quantity of light on the central axis is somewhat large, however,
the irregularity of the quantity of light remains relatively low
even if the dislocation between the sensor and the optical axis of
the entire rod lens array 2 becomes large. That is, when m is 0.94,
the irregularity of the quantity of light is not affected
significantly by the dislocation between the sensor and the optical
axis of the entire rod lens array 2.
[0058] The acceptable irregularity of the quantity of light in a
scanning device is at most 20%. In some applications of use, it is
desirably 15% or less. Furthermore, it is desirable that the margin
for the amount of the dislocation occurring during the assembly is
secured to be about .+-.0.1 mm. In order to satisfy this
requirement, in the case of the rod lens array of R=0.5 mm, it is
desirable that the acceptable range for the amount of the
dislocation is secured to be 0.3 R or more.
[0059] Therefore, as shown in FIG. 6, when the irregularity of the
quantity of light is actually negligible, that is, "when the amount
of the dislocation is 0, the irregularity of the quantity of light
is 15% or less, when the amount of the dislocation is in the range
of 0.3 R or less, the irregularity of the quantity of light is 20%
or less," the overlapping degree m is preferably in the range of
0.91.ltoreq.m.ltoreq.1.01. Furthermore, "when the amount of the
dislocation is the range of 0.3 R or less, the irregularity of the
quantity of light is approximately 15% or less," the overlapping
degree m is preferably in the range of
0.93.ltoreq.m.ltoreq.0.97.
[0060] The values of higher-order coefficients of the refractive
index distribution h.sub.4, h.sub.6, h.sub.8, . . . of 4th-order or
more affect the spherical aberration and field curvature.
Therefore, it is necessary to select the values of h.sub.4,
h.sub.6, h.sub.8, . . . in accordance with the conditions of the
rod lens array so that the average resolution power is optimum.
[0061] In the above-mentioned configuration, as shown in FIG. 7A,
it is desirable that a transparent substrate (cover glass) 5 having
the parallel plane surface is arranged in a manner that the
manuscript plane 3 is located at the front focal position of the
rod lens array 2. According to such a configuration, the manuscript
plane 3 can be set at the front focal position just by putting the
manuscript on the surface of the transparent substrate 5.
Furthermore, in this case, as shown in FIG. 7B, it is desirable
that the parallel plane transparent substrate (cover glass) 5 is
brought into contact with the lens surface of the rod lens array 2.
This can be easily realized by adjusting the thickness of the
transparent substrate (cover glass) 5. According to such a
configuration, the adjustment of the distance between the rod lens
array 2 and the front focal position can be simplified, which makes
the assembly of the optical imaging system cheaper.
[0062] First Example
[0063] Hereinafter, the present invention is described in detail
with reference to the specific Examples. The following Examples and
Comparative Examples use a rod lens array in which a plurality of
columnar rod lenses having a refractive index distribution in the
radial direction are arranged in two rows for one-to-one imaging
with their optical axes in parallel to each other.
[0064] The brightness and irregularity of the quantity of light
were calculated by the use of the equation of the distribution of
the quantity of light for a single rod lens (see Eq. 9 mentioned
above). Furthermore, the modulation transfer function (MTF) values
were calculated by the use of the optical design software "Oslo
Six" by Sinclair Optics (US).
[0065] In Example 1, the distance 2 R between the optical axes of
neighboring rod lenses is 1.085 mm, and the overlapping degree m is
0.930. Specific set values are shown in Table 1, and the
irregularity of the quantity of light when the amount of the
dislocation is .DELTA.X is shown in FIG. 8. The MTF values shown in
Table 1 are for a 12 line-pairs/mm pattern and a 24 line-pairs/mm
pattern. The values are calculated values in the directions of X
and Y at the point of A shown in FIG. 9. As shown in FIG. 8, when
the amount of the dislocation .DELTA.X is within the range of 0.28
R (corresponding to 0.15 mm) or less, the irregularity of the
quantity of light is a practical value of 15% or less.
[0066] In Example 2, the distance 2 R between the optical axes of
neighboring rod lenses is 0.300 mm, and the overlapping degree m is
0.960. Specific set values are shown in Table 1, and the
irregularity of the quantity of light when the amount of the
dislocation is .DELTA.X is shown in FIG. 8. As shown in FIG. 8,
when the amount of the dislocation .DELTA.X is within the range of
0.35 R (corresponding to 0.053 mm) or less, the irregularity of the
quantity of light is a practical value of 15% or less. Since the
acceptable range of amount of the dislocation is in proportion to
R, it is necessary to enhance the assembly precision in Example 2
more than Example 1 wherein R is large.
[0067] In Example 3, the distance 2 R between the optical axes of
neighboring rod lenses is 0.900 mm, and the overlapping degree m is
0.910. Specific set values are shown in Table 2, and the
irregularity of the quantity of light when amount of the
dislocation is .DELTA.X is shown in FIG. 8. As shown in FIG. 8,
when amount of the dislocation .DELTA.X is within the range of 0.20
R (corresponding to 0.09 mm) or less, the irregularity of the
quantity of light is a practical value of 15% or less.
[0068] In Example 4, the distance 2 R between the optical axes of
neighboring rod lenses is 0.100 mm, and the overlapping degree m is
0.970. Specific set values are shown in Table 2, and the
irregularity of the quantity of light when the amount of the
dislocation is .DELTA.X is shown in FIG. 8. As shown in FIG. 8,
when the amount of the dislocation .DELTA.X is within the range of
0.40 R (corresponding to 0.02 mm) or less, the irregularity of the
quantity of light is a practical value of 16% or less.
[0069] In Example 5, the distance 2 R between the optical axes of
neighboring rod lenses is 0.600 mm, and the overlapping degree m is
1.010. Specific set values are shown in Table 3, and the
irregularity of the quantity of light when the amount of the
dislocation is .DELTA.X is shown in FIG. 8. As shown in FIG. 8,
even if the amount of the dislocation .DELTA.X is 0, the
irregularity of the quantity of light is more than 15%. However, in
the wide range wherein the amount of the dislocation .DELTA.X is
within the range of 0.50 R (corresponding to 0.15 mm) or less, the
irregularity of the quantity of light is 20% or less. This may be
practical value depending upon the applications of use.
1 TABLE 1 Example 1 Example 2 Design wavelength 570 nm 570 nm
Center refractive index n.sub.0 1.614 1.639 Coefficient of
refractive index 0.23262 mm.sup.-1 1.56181 mm.sup.-1 distribution g
Coefficient of refractive index +1 +1 distribution h.sub.4
Coefficient of refractive index 0 -4 distribution h.sub.6 Effective
radius of lens r.sub.0 0.5425 mm 0.150 mm n.sub.0 .multidot. g
.multidot. r.sub.0 0.20368 0.38397 Length of lens Z.sub.0 18.386 mm
2.713 mm Z.sub.0/P 0.6807 0.6744 Distance between lenses 2R 1.085
mm 0.300 mm r.sub.0/R 1.00 1.00 Distance between lens and 4.1768 mm
0.6403 mm image L Radius of field of view X.sub.0 1.0090 mm 0.28801
mm Overlapping degree m 0.930 0.960 MTF(%) 12-1 p/mm Y-direction
94.4% 96.7% X-direction 95.7% 97.0% MTF(%) 24-1 p/mm Y-direction
82.4% 87.5% X-direction 84.8% 88.7%
[0070]
2 TABLE 2 Example 3 Example 4 Design wavelength 570 nm 570 nm
Center refractive index n.sub.0 1.450 1.700 Coefficient of
refractive index 0.15000 mm.sup.-1 3.50000 mm.sup.-1 distribution g
Coefficient of refractive index 0 0 distribution h.sub.4
Coefficient of refractive index 0 0 distribution h.sub.6 Effective
radius of lens r.sub.0 0.4000 mm 0.050 mm n.sub.0 .multidot. g
.multidot. r.sub.0 0.0870 0.2975 Length of lens Z.sub.0 27.75 mm
1.207 mm Z.sub.0/P 0.6625 0.6724 Distance between lenses 2R 0.900
mm 0.100 mm r.sub.0/R 0.889 1.00 Distance between lens and 8.2108
mm 0.2795 mm image L Radius of field of view X.sub.0 0.8187 mm
0.09702 mm Overlapping degree m 0.910 0.970 MTF(%) 12-1 p/mm
Y-direction 88.2% 95.8% X-direction 87.2% 95.2% MTF(%) 24-1 p/mm
Y-direction 77.1% 84.1% X-direction 77.4% 82.2%
[0071]
3 TABLE 3 Example 5 Design wavelength 570 nm Center refractive
index n.sub.0 1.800 Coefficient of refractive index 1.000 mm.sup.-1
distribution g Coefficient of refractive index +1 distribution
h.sub.4 Coefficient of refractive index -2 distribution h.sub.6
Effective radius of lens r.sub.0 0.270 mm n.sub.0 .multidot. g
.multidot. r.sub.0 0.468 Length of lens Z.sub.0 4.065 mm Z.sub.0/P
0.6470 Distance between lenses 2R 0.600 mm r.sub.0/R 0.900 Distance
between lens and 1.1165 mm image L Radius of field of view X.sub.0
0.60610 mm Overlapping degree m 1.010 MTF(%) 12-1 p/mm Y-direction
61.9% X-direction 65.9% MTF(%) 24-1 p/mm Y-direction 36.0%
X-direction 35.3%
[0072] In Comparative Example 1, the rod lenses having the same
optical characteristics as Example 1 were used, and the overlapping
degree m was set to be 1.43. Furthermore, in Comparative Example 2,
the rod lenses having the same optical characteristics as Example 2
were used, and the overlapping degree m was set to be 1.50.
Specific values of Comparative Examples 1 and 2 are shown in Table
4.
4 TABLE 4 Co. Ex. 1 Co. Ex. 2 Design wavelength 570 nm 570 nm
Center refractive index n.sub.0 1.614 1.639 Coefficient of
refractive index 0.23262 mm.sup.-1 1.56181 mm.sup.-1 distribution g
Coefficient of refractive index +1 +1 distribution h.sub.4
Coefficient of refractive index 0 -4 distribution h.sub.6 Effective
radius of lens r.sub.0 0.5425 mm 0.150 mm n.sub.0 .multidot. g
.multidot. r.sub.0 0.20368 0.38397 Length of lens Z.sub.0 16.576 mm
2.447 mm Z.sub.0/P 0.6137 0.6083 Distance between lenses 2R 1.085
mm 0.300 mm r.sub.0/R 1.00 1.00 Distance between lens and 7.1379 mm
1.1041 mm image L Radius of field of view X.sub.0 1.5518 mm 0.44969
mm Overlapping degree m 1.430 1.500 MTF(%) 12-1 p/mm Y-direction
82.7% 93.5% X-direction 82.3% 94.0% MTF(%) 12-1 p/mm Y-direction
59.7% 76.7% X-direction 56.1% 77.9% Brightness 75.4 (with 73.6
(with respect to 100 respect to 100 of Example 1) of Example 2) Co.
Ex. = Comparative Example
[0073] "Brightness" in Table 4 refers to an average quantity of
light in the direction of the Y-axis in a case where no dislocation
occurs. The brightness of Examples to which they respectively
correspond are defined as 100.
[0074] In Comparative Examples 1 and 2, the brightness and MTF
value are inferior to the corresponding Examples 1 and 2. This
shows that the quantity of light and resolving power can be
improved according to the present invention.
[0075] (Second Embodiment)
[0076] In this embodiment, by setting the overlapping degree m in
the range of 0.91.ltoreq.m.ltoreq.1.01, the average quantity of
light is increased as compared with those of conventional art, and
the irregularity of the quantity of light is reduced by masking the
lens surface of the rod lens array.
[0077] FIG. 10 is a plan view showing a rod lens array in a second
embodiment according to the present invention. As shown in FIG. 10,
a shading mask 7 having an approximately rectangular shaped opening
portion 7a opening along the longitudinal direction of the rod lens
array 2 is arranged on one side of the rod lens array 2. The
shading mask 7 having such a configuration is preferable because it
is simple and easy to be set.
[0078] An example of the method for setting the shading mask 7
includes the following methods: (1) a method of attaching a metal
or plastic thin plate having a slit to the lens surface of the rod
lens array 2; (2) a method of directly printing the shading portion
of the lens surface of the rod lens array 2 with black ink, etc;
and (3) a method of providing a frame in which the rod lens array 2
is incorporated as a component with a function of a shading mask,
and the like.
[0079] It is desirable that the opening portion 7a of the shading
mask 7 is symmetric to the central axis in the longitudinal
direction of the lens surface of the rod lens array 2. Furthermore,
it is desirable that the half width W of the opening portion 7a of
the shading mask 7 is in the range of ({square root}{fraction
(3/2)}) R+0.1 r.sub.0.ltoreq.W.ltoreq.({square root}{fraction
(3/2)}) R+0.6 r.sub.0, wherein r.sub.0 denotes a radius of the
portion functioning as a lens of the rod lenses 1. When the half
width W of the opening portion 7a of the shading mask 7 is less
than ({square root}{fraction (3/2)}) R+0.1 r.sub.0, the quantity of
light is much lowered. When the half width W is more than ({square
root}{fraction (3/2)}R+0.6 r.sub.0, improvement of the irregularity
of the quantity of light is hardly realized.
[0080] The effect of the shading mask 7 particularly is increased
when the irregularity of the quantity of light is relatively small
even if the shading mask 7 is not provided, that is, the
overlapping degree m is in the range of 0.91.ltoreq.m.ltoreq.1.01
(see First Embodiment above).
[0081] Second Example
[0082] Hereinafter, the present invention is described in detail
with reference to the specific Examples. The following Examples and
Comparative Examples use a rod lens array 2 in which a plurality of
columnar rod lenses 1 having a refractive index distribution in the
radial direction are arranged in two rows for one-to-one imaging
with their optical axes 1a in parallel to each other.
[0083] In Examples and Comparative Examples, the distance 2 R
between the optical axes of neighboring rod lenses is 1.000 mm, and
the overlapping degree m is 0.940. Specific set values are shown in
Table 5.
5 TABLE 5 Example 6,7,8,9, Co. Ex. 3 Design wavelength 570 nm
Center refractive index n.sub.0 1.600 Coefficient of refractive
index 0.2618 mm.sup.-1 distribution g Coefficient of refractive
index +1 distribution h.sub.4 Coefficient of refractive index -10
distribution h.sub.6 Effective radius of lenses r.sub.0 0.500 mm
n.sub.0 .multidot. g .multidot. r.sub.0 0.20944 Length of lens
Z.sub.0 16.285 mm Z.sub.0/P 0.678 Distance between lenses 2R 1.000
mm r.sub.0/R 1.00 Distance between lens and image L 3.800 mm Radius
of field of view X.sub.0 0.940 mm Overlapping degree m 0.940
[0084] In Example 6, the half width W of the opening portion 7a of
the shading mask 7 is expressed by W=1.3 R=({square root}{fraction
(3/2)}) R+0.434 r.sub.0. In Example 7, W=1.1 R=({square
root}{fraction (3/2)}) R+0.234 r.sub.0; in Example 8, W=1.466
R=({square root}{fraction (3/2)}) R+0.600 r.sub.0; in Example 9,
W=0.966 R=({square root}{fraction (3/2)}) R+0.100 r.sub.0. In
Comparative Example 3, the shading mask 7 is not provided. The
irregularity of the quantity of light in each case was calculated
when the dislocation does not occur and when amount of the
dislocation is .DELTA.X=0.3 R. The calculated results are shown in
Tables 6 and 7 and FIGS. 11, 12, 13 and 14.
6 TABLE 6 Co. Ex. 3 (without mask) Example 6 Example 7 Amount of 0
0.3R 0 0.3R 0 0.3R dislocation .DELTA.X Average 100.00 97.03 97.94
92.79 87.02 84.33 quantity of light Maximum 106.52 101.80 104.44
96.82 92.76 88.32 quantity of light Minimum 95.74 89.34 93.69 86.31
83.24 79.49 quantity of light Irregularity of 11.26 13.95 11.47
12.18 11.44 11.11 quantity of light (%)
[0085]
7 TABLE 7 Example 8 (without mask) Example 9 Amount of 0 0.3R 0
0.3R dislocation .DELTA.X Average quantity of 100.00 96.56 78.16
74.84 light Maximum quantity 106.52 101.26 83.18 78.11 of light
Minimum quantity 95.74 88.98 74.77 71.26 of light Irregularity of
11.26 13.80 11.24 9.61 quantity of light (%)
[0086] The quantity of light is evaluated by the use of the optical
design software "Oslo Six" by Sinclair Optics (US). The number of
light beams reaching the image surface emitted from the light
source is defined as "brightness." Furthermore, the average
quantity of light (=100) in Comparative Example 3 without
dislocation was defined as the standard of the quantity of
light.
[0087] As shown in the above Tables 6, and 7 and in FIGS. 11, 12,
13, and 14, the irregularity of the quantity of light at amount of
dislocation .DELTA.X of 0.3 R reaches 13.95% in Comparative Example
3. However, in Examples 6 to 9, the irregularity of the quantity of
light was improved by 12.18%, 11.11%, 13.80% and 9.61%,
respectively. On the other hand, when no dislocation occurs, the
irregularity of the quantity of light almost is not changed even if
the shading mask 7 is provided.
[0088] The deterioration of the average quantity of light with
respect to the case where the shading mask is not provided
(Comparative Example 3) is, 2% in Example 6, 13% in Example 7, 0%
in Example 8 and 22% in Example 9 (in any of these cases, no
dislocation occurs). It is effective to the application of use
where the irregularity of the quantity of light is smaller than the
average quantity of light.
[0089] In the Second Embodiment of the present invention, the
values of R and m are not limited to the values shown in the
Examples. It is desirable that the values of R and m are within the
same range as those of the First Embodiment.
[0090] The invention may be embodied in other specific forms
without departing from the spirit or essential characteristics
thereof. The embodiments disclosed in this application are to be
considered in all respects as illustrative and not restrictive, the
scope of the invention being indicated by the appended claims
rather than by the foregoing description, all changes that come
within the meaning and range of equivalency of the claims are
intended to be embraced therein.
* * * * *