U.S. patent application number 09/435193 was filed with the patent office on 2002-10-10 for projection lens.
Invention is credited to OKUYAMA, ATSUSHI.
Application Number | 20020145809 09/435193 |
Document ID | / |
Family ID | 18282989 |
Filed Date | 2002-10-10 |
United States Patent
Application |
20020145809 |
Kind Code |
A1 |
OKUYAMA, ATSUSHI |
October 10, 2002 |
PROJECTION LENS
Abstract
A projection lens arranged to project an image formed on a
display panel onto a screen includes a plurality of lens units
movable along an axis for varying magnification, wherein at least
one of lenses constituting the plurality of lens units has at least
one lens surface of shape having no symmetry with respect to the
axis, so that the trapezoidal deformation which tends to occur when
the image formed on the display panel is projected onto the screen
is corrected well.
Inventors: |
OKUYAMA, ATSUSHI;
(TOKOROZAWA-SHI, JP) |
Correspondence
Address: |
MICHAEL M. MURRAY
MORGAN & FINNEGAN L.L.P.
345 PARK AVENUE
NEW YORK
NY
10154
US
|
Family ID: |
18282989 |
Appl. No.: |
09/435193 |
Filed: |
November 8, 1999 |
Current U.S.
Class: |
359/649 ;
359/651; 359/691 |
Current CPC
Class: |
G02B 15/1425
20190801 |
Class at
Publication: |
359/649 ;
359/651; 359/691 |
International
Class: |
G02B 003/00; G02B
009/00; G02B 003/02; G02B 015/14 |
Foreign Application Data
Date |
Code |
Application Number |
Nov 10, 1998 |
JP |
10-334944 |
Claims
1. A projection lens arranged to project an image formed on a
display panel onto a screen, said projection lens comprising: a
plurality of lens units movable along an axis for varying
magnification, wherein at least one of lenses constituting said
plurality of lens units has at least one lens surface of shape
having no symmetry with respect to the axis.
2. A projection lens according to claim 1, wherein said display
panel and the axis are almost orthogonal with each other, and a
center of said display panel is offset from the axis.
3. A projection lens according to claim 1, satisfying the following
condition: -5.degree.<.theta.<5.degree.where .theta. is an
angle which a normal of said display panel makes with the axis.
4. An apparatus according to claim 1, wherein at least one of the
lenses constituting said plurality of lens units has at least one
aspheric surface of shape having symmetry with respect to the
axis.
5. A projection lens according to claim 1, wherein said projection
lens comprises, in order from the screen side, a negative lens unit
having a negative refractive power and a positive lens unit having
a positive refractive power.
6. A projection lens according to claim 5, wherein said negative
lens unit has a lens surface of shape having no symmetry with
respect to the axis.
7. A projection lens according to claim 5, wherein said negative
lens unit comprises, in order from the screen side, a lens subunit
of meniscus form convex toward the screen side, a lens subunit of
bi-concave form, and a lens subunit of bi-convex form.
8. A projection lens according to claim 7, wherein said lens
subunit of meniscus form has a lens surface, facing the screen
side, of shape having no symmetry with respect to the axis.
9. A projection lens according to claim 5, wherein said positive
lens unit has an aspheric surface having symmetry with respect to
the axis.
Description
BACKGROUND OF THE INVENTION
[0001] 1. Field of the Invention
[0002] The present invention relates to projection lenses and image
projection apparatuses using the same and, more particularly, to
projection lenses suited to, for example, liquid crystal projectors
of the type in which an original projection image displayed on a
display panel, such as a liquid crystal display element, is
projected obliquely onto a screen in an enlarged size. Still more
particularly, the present invention relates to such a liquid
crystal projector that has a projection lens appropriately designed
to correct well the distortion and trapezoidal deformation of the
projected image and the declination of the image plane so that a
projected image of good quality can be obtained.
[0003] 2. Description of Related Art
[0004] Heretofore, there have been proposed a variety of projection
apparatuses arranged to project an original projection image
displayed on a display panel, such as a liquid crystal display
element, onto a screen.
[0005] FIG. 21 is a diagram of geometry of the arrangement of a
projection apparatus of the oblique projection type in which an
original projection image LCD is obliquely projected onto a screen
S by a projection lens LP.
[0006] In the projection apparatus shown in FIG. 21, for the
purpose of preventing the projected image from being distorted when
the original projection image LCD is projected on the screen S, the
so-called image frame shifting is utilized in which the center LCDa
of the original projection image LCD is shifted downward with
respect to an optical axis Ax of the projection lens LP.
[0007] In the conventional liquid crystal projector, when installed
in the apparatus, despite a short projection distance as usual, the
projected image has to appear more upper. To this purpose, the
projection lens is made wider in the image angle. The center of the
liquid crystal panel is thus allowed to take an offset (shifted)
position relative to the optical axis of the projection lens, so
that the center of the projected image appears upper than the
optical axis of the projection lens.
[0008] However, when the image angle of the projection lens is
widened, distortion, field curvature, lateral chromatic aberration
and other aberrations become larger, causing an increase of the
difficulty of correcting these various aberrations.
[0009] Particularly with the distortion left large, because the
projected image is offset from the optical axis, the projected
image is distorted asymmetrically in the vertical direction, giving
rise to a problem of detracting the quality of the projected
image.
[0010] To solve this problem, among others, a method of introducing
an axially-symmetric aspheric surface into the projection lens,
too, has been put into practice. However, since the original
projection image LCD is offset as shown in FIG. 22, it is difficult
correct the distortion throughout an image circle IC including the
entirety of the original projection image LCD.
BRIEF SUMMARY OF THE INVENTION
[0011] It is an object of the present invention to provide, by
using an aspheric surface having no axial symmetry in a part of an
optical system, a projection lens which can correct trapezoidal
deformation and distortion as an original projection image is
projected obliquely, and an image projection apparatus using such a
projection lens.
[0012] To attain the above object, in accordance with an aspect of
the invention, there is provided a projection lens arranged to
project an image formed on a display panel onto a screen, the
projection lens comprising a plurality of lens units movable along
an axis for varying magnification, wherein at least one of lenses
constituting the plurality of lens units has at least one lens
surface of shape having no symmetry with respect to the axis.
[0013] Further, in the above projection lens, the display panel and
the axis are almost orthogonal with each other, and a center of the
display panel is offset from the axis.
[0014] Further, in the above projection lens, a normal of the
display panel makes an angle .theta. with the axis, wherein the
following condition is satisfied:
-5.degree.<.theta.<5.degree.
[0015] Further, in the above projection lens, at least one of
lenses constituting the plurality of lens units has at least one
aspheric surface of shape having symmetry with respect to the
axis.
[0016] Further, the above projection lens comprises, in order from
the screen side, a negative lens unit having a negative refractive
power and a positive lens unit having a positive refractive
power.
[0017] Further, in the above projection lens, the negative lens
unit has a lens surface of shape having no symmetry with respect to
the axis.
[0018] Further, in the above projection lens, the negative lens
unit comprises, in order from the screen side, a lens subunit of
meniscus form convex toward the screen side, a lens subunit of
bi-concave form, and a lens subunit of bi-convex form.
[0019] Further, in the above projection lens, the lens subunit of
meniscus form has a lens surface, facing the screen side, of shape
having no symmetry with respect to the axis.
[0020] Further, in the above projection lens, the positive lens
unit has an aspheric surface having symmetry with respect to the
axis.
[0021] The above and further objects and features of the invention
will become apparent from the following detailed description of
preferred embodiments thereof taken in conjunction with the
accompanying drawings.
BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING
[0022] FIG. 1 is a longitudinal section view of a numerical example
1 of the lens of the invention.
[0023] FIG. 2 is a longitudinal section view of a numerical example
2 of the lens of the invention.
[0024] FIG. 3 is a longitudinal section view of a numerical example
3 of the lens of the invention.
[0025] FIG. 4 is a longitudinal section view of a numerical example
4 of the lens of the invention.
[0026] FIG. 5 shows graphic representations of the aberrations in
the numerical example 1 of the invention in the wide-angle end.
[0027] FIG. 6 shows graphic representations of the aberrations in
the numerical example 1 of the invention in the telephoto end.
[0028] FIG. 7 is a plan view for explaining the distortion in the
numerical example 1 of the invention.
[0029] FIG. 8 shows graphic representations of the aberrations in
the numerical example 2 of the invention in the wide-angle end.
[0030] FIG. 9 shows graphic representations of the aberrations in
the numerical example 2 of the invention in the telephoto end.
[0031] FIG. 10 is a plan view for explaining the distortion in the
numerical example 2 of the invention.
[0032] FIG. 11 shows graphic representations of the aberrations in
the numerical example 3 of the invention in the wide-angle end.
[0033] FIG. 12 shows graphic representations of the aberrations in
the numerical example 3 of the invention in the telephoto end.
[0034] FIG. 13 is a plan view for explaining the distortion in the
numerical example 3 of the invention.
[0035] FIG. 14 shows graphic representations of the aberrations in
the numerical example 4 of the invention in the wide-angle end.
[0036] FIG. 15 shows graphic representations of the aberrations in
the numerical example 4 of the invention in the telephoto end.
[0037] FIG. 16 is a plan view for explaining the distortion in the
numerical example 4 of the invention.
[0038] FIG. 17 is a diagram for explaining an original projection
image in view of the distortion according to the invention.
[0039] FIG. 18 is a plan view for explaining the distortion
according to the invention.
[0040] FIG. 19 is an enlarged view of FIG. 4.
[0041] FIG. 20 is a graph for explaining the coordinates for the
lens surface of the projection lens according to the invention.
[0042] FIG. 21 is a diagram for explaining the conventional liquid
crystal projector.
[0043] FIG. 22 is a plan view for explaining a part of the liquid
crystal projector shown in FIG. 21.
DETAILED DESCRIPTION OF THE INVENTION
[0044] Hereinafter, preferred embodiments of the invention will be
described in detail with reference to the drawings.
[0045] FIGS. 1 to 4 in block diagram show numerical examples 1 to 4
of the lens of the invention, whose data will be given later.
[0046] In FIGS. 1 to 4, a projection lens (projection optical
system) LP, an optical block G, such as an optical filter, a color
separation prism, etc., and a projection image LCD formed on a
display panel, such as a liquid crystal element, are arranged in
this order from a screen S.
[0047] Further, reference character ZRN denotes an aspheric surface
having no axial symmetry, and reference character ASP denotes an
axially-symmetric aspheric surface. The projection lens LP has a
lens unit L1 of negative refractive power and a lens unit L2 of
positive refractive power, both of which axially move toward the
screen S, while decreasing the separation therebetween, to vary the
focal length from the wide-angle end to the telephoto end.
Accordingly, the size of the projected image on the screen S is
made variable. Further, a fixed lens (r17 - r18) is disposed
immediately before the optical block G.
[0048] The center LCDa of the projection image LCD is shifted
(decentered in parallel) from an optical axis (reference axis) Ax
of the projection lens LP.
[0049] In the numerical examples 1 to 3, as shown in FIGS. 1 to 3,
the screen S and the projection image LCD are parallel to each
other, and both the screen S and the projection image LCD are
perpendicular to the optical axis Ax of the projection lens LP. The
projection lens LP projects the projection image LCD onto the
screen S in enlarged scale at various magnifications.
[0050] In the numerical example 4, as shown in FIG. 4, while the
projection image LCD is perpendicular to the optical axis Ax of the
projection lens LP, the optical axis Ax of the projection lens LP
is made tilted with respect to the screen S, (or the optical axis
Ax is made to have a predetermined angle .alpha. with the normal Sa
of the screen S).
[0051] Further, in the numerical examples 1 to 4, with the use of
the aspheric surfaces ZRN and ASP mentioned before, the distortion
produced by the oblique projection is corrected. (Incidentally, the
term "reference axis (reference optical axis)" used in the
invention means an optical axis specified by at least two lens
surfaces in the projection lens LP.) The projection lens LP
projects the projection image LCD onto the screen S in enlarged
scale at various magnifications.
[0052] FIGS. 5 to 7 show the lateral aberrations of the numerical
example 1 in the wide-angle end and in the telephoto end and a
lattice used for explaining the state of distortion.
[0053] FIGS. 8 to 10 show the lateral aberrations of the numerical
example 2 in the wide-angle end and in the telephoto end and a
lattice used for explaining the state of distortion.
[0054] FIGS. 11 to 13 show the lateral aberrations of the numerical
example 3 in the wide-angle end and in the telephoto end and a
lattice used for explaining the state of distortion.
[0055] FIGS. 14 to 16 show the lateral aberrations of the numerical
example 4 in the wide-angle end and in the telephoto end and a
lattice used for explaining the state of distortion.
[0056] The lateral aberrations are concerned with a central point
P1 and two corners P2 and P3 in the projection image LCD, as shown
in FIG. 17, and calculated by tracing rays of light from the screen
S to the projection image LCD. The distortion represents the
projection image itself when rays of light are traced from the
projection image LCD to the screen S.
[0057] The first lens unit L1 of the projection lens LP is composed
of, in order from the screen side (longer conjugate point), a lens
(r1-r2) of meniscus form convex toward the screen side, a negative
lens (r3-r4) of bi-concave form and a positive lens (r5-r6) of
bi-convex form.
[0058] The second lens unit L2 of the projection lens LP is
composed of, in order from the screen side (longer conjugate
point), a positive lens (r7-r8) having a convex surface facing the
projection image LCD (shorter conjugate point), a positive lens
(r9-r10) having a convex surface facing the screen side, a negative
lens (r11-r12) of bi-concave form, a positive lens (r13-r14) having
a convex surface facing the screen side, and a positive lens
(r15-r16) of bi-convex form.
[0059] Then, in the numerical example 1, a lens surface r1, facing
the screen side, of the lens L11 is made to be an aspheric surface
having no axial symmetry.
[0060] Also, in the numerical example 2, a lens surface r2, facing
the projection image LCD, of the lens L11 is made to be an aspheric
surface having no axial symmetry, and, in the numerical example 3,
a lens surface r17, facing the screen side, of the positive lens
L26 is made to be an aspheric surface having no axial symmetry.
[0061] Also, in the numerical example 4, both lens surfaces r1 and
r2 of the lens L11 and both lens surfaces r17 and r18 of the
positive lens L26 each are made to be an aspheric surface having no
axial symmetry.
[0062] In the present invention, at least one of the surfaces
constituting the projection lens LP is provided with an aspheric
surface having no axial symmetry, so that it is possible to choose,
for the design purposes, only an area corresponding to the liquid
crystal panel LCD which is offset.
[0063] By this arrangement, despite a few lens surfaces, the
distortion can be corrected well. Particularly, for the lens
members on the enlarge projection side of the projection lens (that
is, the ones nearest to the screen), and for the lens members
nearest to the liquid crystal panel, the light beam utilizes only
the upper or lower parts of the lens members. On this account, such
places are selected to use the aspheric surface or surfaces having
no axial symmetry, thus effectively correcting various aberrations
(especially, distortion).
[0064] In the numerical examples 1 to 3, the projection lens LP
(with exclusion of the aspheric surface having no axial symmetry)
has its optical axis Ax set perpendicular to the enlarge projection
plane (screen) S and the liquid crystal panel LCD.
[0065] In order to project the image even more upward onto the
screen S, the liquid crystal projector is raised at its end nearest
to the screen, being tilted upward. In this situation, as shown in
FIG. 18, in addition to the corrected distortion, the projection
lens LP produces a trapezoidal deformation due to the tilting.
[0066] The numerical example 4 is, as shown in FIG. 19 in the
extended form, an example of design for the projection lens LP when
used with its optical axis Ax tilted with respect to the enlarge
projection plane (screen) S, while still permitting the resultant
distortion to be corrected.
[0067] In FIG. 19, the reference axis (optical axis) Ax makes an
angle of .alpha.=8.degree. with a normal Sa of the screen S at the
cross point S1 of the screen surface and the reference axis Ax, and
the liquid crystal panel LCD is put below the normal Sa with the
cross point LCDa of the liquid crystal panel and the reference axis
Ax set at a distance of .DELTA.Y=534.5 mm.
[0068] In this connection, it should be noted that, in the
projection lens according to the invention, if an angle .theta.
which the reference axis (reference optical axis) of the projection
lens makes with the normal of the display panel LCD lies within the
following range:
-5.degree.<.theta.<5.degree.,
[0069] an image displayed on the display panel LCD can be projected
well onto the screen S.
[0070] Next, four numerical examples 1 to 4 of the invention are
shown. In the numerical data for the examples 1 to 4, ri is the
radius of curvature of the i-th lens surface, when counted from the
enlarge projection side, di is the i-th axial lens thickness or air
separation, when counted from the enlarge projection side, and ndi
and vdi are respectively the refractive index and Abbe number of
the i-th lens element.
[0071] The shape of an aspheric surface having axial symmetry is
expressed in the coordinates with a z axis in the optical axis
direction and a height h in the direction perpendicular to the
optical axis, the direction from the screen to the display panel
being taken as positive, by the following equation:
z=+Ah.sup.4+Bh.sup.6+Ch.sup.8+Dh.sup.10Eh.sup.12
[0072] where C is the curvature of the osculating sphere, and K, A,
B, C, D and E are the aspheric coefficients.
[0073] The shape of an aspheric surface having no axial symmetry is
expressed in the coordinates with a z axis in the optical axis
direction, a y axis in the direction perpendicular to the optical
axis, and an x axis in the direction perpendicular to the z and y
axes, the direction from the screen to the display panel being
taken as positive, by the following equation: 1 z = c ( x 2 + y 2 )
1 + 1 - ( 1 + K ) c 2 ( x 2 + y 2 ) + j zj p j
[0074] where c is the curvature of the osculating sphere, K and zj
are the aspheric coefficients, and
p.sub.3=y
p.sub.4=x.sup.2-y.sup.2
p.sub.5=2x.sup.2+2y.sup.2-1
p.sub.9=3x.sup.2y+3y.sup.3-2y
p.sub.103x.sup.2y-y.sup.3
p.sub.11=x.sup.4=6x.sup.2y.sup.2+y.sup.4
p.sub.12=4x.sup.4-4y.sup.4-3x.sup.2+3y.sup.2
p.sub.13=6x.sup.4+12x.sup.2y.sup.2+6y.sup.4-6x.sup.2-6y.sup.2+1
p.sub.23=6x.sup.6-30x.sup.4y.sup.2-30x.sup.2y.sup.4+6y.sup.6-5x.sup.4+30x.-
sup.2y.sup.2-5y.sup.4
p.sub.24=15x.sup.6+15x.sup.4y.sup.2-15x.sup.2y.sup.4-15y.sup.6-20x.sup.4+2-
0y.sup.46x.sup.2-6y.sup.2
p.sub.25=20x.sup.6+60x.sup.4y.sup.2+60x.sup.2y.sup.4+20y.sup.6-30x.sup.4-6-
0x.sup.2y.sup.4-30y.sup.4+12x.sup.2+12y.sup.2+1.
[0075] In each numerical example, taking a common axis of symmetry
of all the spherical surfaces as the reference axis, the aspheric
surface having no axial symmetry has its original point of the
equation for the shape lying not on this reference axis, or moved
therefrom in coordinates as shown in FIG. 20. Therefore, data of
the original point of the equation for the shape of the aspheric
surface having no axial symmetry are described as decentering data
together with the lens data.
1 Numerical Example 1: f:47.2.about.73.2 Fno:2.51.about.3.69
.omega.x: 15.63.about.10.22 .omega.y: 19.72.about.13.01 r d nd
.nu.d 1 Asphere 4.20 1.492 57.4 2 26.141 24.99 3 -24.377 2.00 1.581
40.8 4 63.361 0.18 5 66.940 4.28 1.805 25.4 6 -84.774 Variable 7
894.781 3.58 1.603 60.7 8 -91.106 0.20 9 42.480 5.15 1.639 55.4 10
367.733 20.58 11 -56.665 2.50 1.741 27.8 12 45.375 1.02 13 69.625
4.31 1.492 57.4 14 Asphere 2.98 15 84.679 9.45 1.516 64.1 16
-40.811 Variable 17 111.360 6.00 1.516 64.1 18 -216.146 9.98 19
inf. 40.00 1.516 64.1 20 inf. Variable Zooming Position Separation
W T d 6 15.56 3.00 d16 39.48 90.96
[0076]
2 Aspheric Coefficients of aspheric surface having axial symmetry:
For r14, c(1/r) : -2.641e - 03 K: -1.345e + 01 A: 4.626e - 06 B:
1.900e - 10 C: 7.502e - 13 D: -8.734e - 15 E: 0.000e + 00 Aspheric
Coefficients of aspheric surface having no axial symmetry: For r 1,
c(1/r) : 1.753e - 02 K: 3.886e + 00 z 4: -9.177e - 07 z 5: 2.131e -
05 z11: 3.457e - 09 z12: 1.826e - 09 z13: 3.898e - 07 z23: -3.750e
- 12 z24: -1.587e - 12 z25: -2.517e - 12
[0077]
3 Numerical Example 2: f: 47.2.about.73.2 Fno: 2.51.about.3.69
.omega.x: 15.63.about.10.22 .omega.y: 19.72.about.13.01 r d nd
.nu.d 1 Asphere 4.20 1.49 57.4 2 Asphere 24.89 3 -24.294 2.00 1.581
40.8 4 62.607 0.17 5 66.026 4.29 1.805 25.4 6 -85.178 Variable 7
1075.082 3.60 1.603 60.7 8 -92.697 0.20 9 42.537 5.23 1.639 55.4 10
455.826 20.43 11 -56.178 2.50 1.741 27.8 12 45.490 0.98 13 68.240
4.33 1.492 57.4 14 Asphere 3.09 15 85.674 9.44 1.516 64.1 16
-40.755 Variable 17 111.796 5.99 1.516 64.1 18 -216.795 9.98 19
inf. 40.00 1.516 64.1 20 inf. Variable Zooming Position Separation
W T d 6 15.49 3.00 d16 39.66 91.18
[0078]
4 Aspheric Coefficients ofaspheric surface having axial symmetry:
For r 1, c(1/r) : 1.815e - 02 K: 3.645e + 00 A: 2.058e - 06 B:
-2.203e - 10 C: 7.966e - 13 D: 0.000e + 00 E: 0.000e + 00 For r14,
c(1/r) : -2.616e - 03 K: -7.274e + 01 A: 4.638e - 06 B: 4.770e - 10
C: -3.106e - 14 D: -7.398e - 15 E: 0.000e + 00 Aspheric
Coefficients of aspheric surface having no axial symmetry: For r 2,
c(1/r): 3.900e - 02 K: 9.493e - 02 z 3: -2.911e - 05 z 4: -1.614e -
07 z 5: -2.193e - 05 z13: 1.782e - 07 z25: -9.723e - 11
[0079]
5 Numerical Example 3: f: 47.2.about.73.1 Fno:2.57.about.3.73
.omega.x: 15.64.about.10.23 .omega.y: 19.73.about.13.02 r d nd
.nu.d 1 Asphere 4.20 1.492 57.4 2 28.832 22.20 3 -23.880 2.00 1.581
40.8 4 68.612 0.22 5 73.835 4.62 1.805 25.4 6 -73.326 Variable 7
9046.483 4.31 1.603 60.7 8 -98.245 0.20 9 41.994 6.51 1.639 55.4 10
1023.504 18.90 11 -57.529 2.50 1.741 27.8 12 43.285 0.73 13 55.926
4.45 1.492 57.4 14 Asphere 3.05 15 79.980 9.27 1.516 64.1 16
-42.281 Variable 17 Asphere 5.78 1.492 57.4 18 -102.863 9.98 19
inf. 40.00 1.516 64.1 20 inf. Variable Zooming Position Separation
W T d 6 15.57 3.00 d16 41.86 92.49
[0080]
6 Aspheric Coefficients of aspheric surface having axial symmetry:
For r 1, c(1/r): 1.166e - 02 K: 1.048e + 01 A: 2.887e - 06 B:
-3.749e - 10 C: 9.292e - 13 D: 0.000e + 00 E: 0.000e + 00 For r14,
c(1/r): -1.952e - 04 K: -5.410e + 04 A: 5.199e - 06 B: 1.646e - 09
C: -4.933e - 12 D: -6.981e - 16 E: 0.000e + 00 Aspheric
Coefficients ofaspheric surface having no axial symmetry: For r17,
c(1/r): 4.518e - 03 K: -5.813e + 01 z 2: -2.594e - 05 z 4: -2.346e
- 08 z 5: -8.619e - 05 z11: -7.525e - 10 z12: 9.041e - 11 z13:
2.958e - 08 z23: -1.454e - 13 z24: -1.311e - 14 z25: -1.094e -
11
[0081]
7 Numerical Example 4: f: 47.2.about.73.2 Fno: 2.51.about.3.60
.omega.x: 15.63.about.10.23 .omega.y: 19.72.about.13.01 r d nd
.nu.d 1 Asphere 4.20 1.492 57.4 2 Asphere 22.46 3 -23.833 2.00
1.581 40.8 4 68.512 0.82 5 81.776 4.63 1.805 25.4 6 -75.185
Variable 7 -6266.770 3.27 1.603 60.7 8 -107.530 0.20 9 42.619 7.11
1.639 55.4 10 -550.693 17.56 11 -52.483 2.50 1.741 27.8 12 45.852
0.80 13 64.287 4.47 1.492 57.4 14 Asphere 4.28 15 99.741 9.43 1.516
64.1 16 -42.096 Variable 17 Asphere 5.83 1.516 64.1 18 Asphere 9.98
19 inf. 40.00 1.516 64.1 20 inf. Variable Zooming Position
Separation W T d 6 15.99 3.00 d16 40.59 90.11
[0082]
8 Aspheric Coefficients of aspheric surface having axial symmetry:
For r14, c(1/r): -3.465e - 03 K: -1.157e + 01 A: 4.676e - 06 B:
1.461e - 09 C: -4.218e - 12 D: -2.289e - 16 E: 0.000e + 00 Aspheric
Coefficients of aspheric surface having no axial symmetry: For r 1,
c(1/r): 1.550e - 02 K: 5.961e + 00 z 3: 6.129e - 03 z 4: -3.581e -
06 z 5: 2.009e - 04 z 9: -3.693e - 07 z10: 7.064e - 07 z11: 4.792e
- 07 z12: 2.189e - 08 z13: 2.960e - 07 z23: 1.450e - 11 z24:
-6.346e - 12 z25: -6.194e - 11 For r 2, c(1/r): 3.615e - 02 K:
0.000e + 00 z 5: 1.658e - 04 z 9: -2.011e - 06 z10: 7.746e - 07
z11: 5.342e - 07 z12: 1.973e - 08 z13: -1.911e - 07 z23: 1.228e -
10 z24: -1.137e - 14 z25: -1.873e - 10 For r17, c(1/r): 6.412e - 04
K: 0.000e + 00 z 5: 3.949e - 04 z 9: -3.517e - 06 z10: 1.393e - 06
z11: 3.622e - 07 z12: 1.017e - 08 z13: 1.276e - 07 z23: 1.745e - 10
z24: -2.981e - 11 z25: 4.313e - 11 For r18, c(1/r): -1.274e - 02 K:
0.000e + 00 z 5: 5.047e - 04 z 9: -3.272e - 06 z10: 4.507e - 07
z11: 4.402e - 07 z12: 1.430e - 08 z13: 3.482e - 07 z23: 1.704e - 10
z24: -2.876e - 11 z25: 3.458e - 11 Decentering data: r dy (mm)
.beta.(degree) 1 0.11 0.06 2 0.06 0.50 17 1.36 1.32 18 1.64
0.02
[0083] It will be appreciated from the foregoing that, according to
the invention, an aspheric surface having no axial symmetry is
employed in part of the optical system. It is, therefore, made
possible to achieve a projection lens which, when projecting the
image obliquely, corrects well the trapezoidal deformation and
distortion, and an image projection apparatus using the same.
* * * * *