U.S. patent application number 10/235916 was filed with the patent office on 2003-10-02 for objective for optical disk, optical pickup, optical disk writer-reader, and optical disk reader.
Invention is credited to Itonaga, Makoto.
Application Number | 20030184881 10/235916 |
Document ID | / |
Family ID | 27555001 |
Filed Date | 2003-10-02 |
United States Patent
Application |
20030184881 |
Kind Code |
A1 |
Itonaga, Makoto |
October 2, 2003 |
Objective for optical disk, optical pickup, optical disk
writer-reader, and optical disk reader
Abstract
An objective for an optical disk is made of a single
double-sided aspherical lens having a numerical aperture (NA) equal
to or greater than 0.75 and capable of minimizing axial aberration,
off-axis aberration, surface-to-surface eccentricity aberration,
and chromatic aberration. The objective (11) has a first aspherical
surface (1). The vertex of the first surface has a radius of
curvature R1 defined as follows:
0.95.multidot.A<R1<1.05.multidot.A A=B/C B=0.85f(n-1)
C=n(0.60866-0.11.multidot.t/f-0.1272.multidot.d/f)(0.83+0.2.multidot.NA)
where n is a refractive index of the lens, f is a focal length of
the lens, t is a thickness along optical axis through the center of
the lens and d is the thickness of a transmission layer of the
optical disk.
Inventors: |
Itonaga, Makoto;
(Kanagawa-ken, JP) |
Correspondence
Address: |
NATH & ASSOCIATES
1030 15th STREET
6TH FLOOR
WASHINGTON
DC
20005
US
|
Family ID: |
27555001 |
Appl. No.: |
10/235916 |
Filed: |
September 6, 2002 |
Current U.S.
Class: |
359/719 ;
G9B/7.102; G9B/7.12 |
Current CPC
Class: |
G11B 7/13922 20130101;
G11B 7/139 20130101; G11B 7/1374 20130101 |
Class at
Publication: |
359/719 |
International
Class: |
G02B 003/02; G02B
013/18 |
Foreign Application Data
Date |
Code |
Application Number |
Sep 21, 2001 |
JP |
P2001-289992 |
Sep 21, 2001 |
JP |
P2001-290001 |
Apr 19, 2002 |
JP |
P2002-118318 |
Apr 19, 2002 |
JP |
P2002-118489 |
Jul 5, 2002 |
JP |
P2002-197990 |
Jul 5, 2002 |
JP |
P2002-197996 |
Claims
What is claimed is:
1. An objective for an optical disk comprising a single lens,
wherein the objective has first and second aspherical surfaces, a
numerical aperture (NA) of the objective is equal to or greater
than 0.75 and a radius of curvature R1 at a vertex of the first
surface is defined as
follows:0.95.multidot.A<R1<1.05.multidot.A,A=B/C,B=0.85f(n-1)
andC=n(0.60866-0.11.multidot.t/f-0.1272.multidot.d/f)(0.83+0.2.multidot.N-
A)where n is a refractive index of the objective, f is a focal
length of the objective, t is a thickness along optical axis
through the center of the objective and d is the thickness of a
transmission layer of the optical disk.
2. The objective of claim 1, wherein the thickness t is equal to or
greater than the focal length f.
3. The objective of claim 1, wherein the objective has an image
magnification of 0.
4. The objective of claim 1, wherein incident rays on the objective
from a light source have a wavelength equal to of less than 450
nm.
5. An optical pickup comprising: the objective of claim 1; a laser
source; and a photodetector.
6. The optical pickup of claim 5, wherein a working distance of the
objective depends on the diameter of an optical disk irradiated
with a laser beam emitted from the laser source and is defined as
follows:working distance>0.005.times.optical disk radius
7. An optical disk writer-reader comprising: the optical pickup of
claim 5; and a write-read unit to write and read information to and
from an optical disk through the pickup.
8. An optical disk reader comprising: the optical pickup of claim
5; and a read unit to read information from an optical disk through
the optical pickup.
9. An objective for an optical disk comprising a single lens,
wherein the objective has first and second aspherical surfaces, a
numerical aperture (NA) of the objective is equal to or greater
than 0.75 and an angle u1' between a highest ray passing through
the objective and an optical axis satisfies the following
condition:0.94.multidot.K<sin(u1')<1.06.mul- tidot.K
andK=(0.60866-0.11.multidot.t/f-0.1272.multidot.d/f)(0.83+0.2.mult-
idot.NA).multidot.NA/0.85where f is a focal length of the
objective, t is a thickness along optical axis through center of
the objective and d is the thickness of a transmission layer of the
optical disk.
10. An objective for an optical disk comprising a single lens,
wherein the lens has first and second aspherical surfaces, a
numerical aperture (NA) of the objective is equal to or greater
than 0.75 and an angle between a normal to the first surface at a
point where a highest ray enters the first surface and an optical
axis is equal to or less than 57 degrees.
11. An objective for an optical disk comprising a single lens,
wherein the objective has first and second aspherical surfaces, a
numerical aperture (NA) of the objective is equal to or greater
than 0.75 and an angle .theta. between a normal to the first
surface at a point where a highest ray enters the and an optical
axis satisfies the following
condition:.theta.<57-47.3.multidot.(0.85-NA)(degrees).
12. The objective of claim 9, wherein the thickness t is equal to
or greater than the focal length f.
13. The objective of claim 9, wherein the objective has an image
magnification of 0.
14. The objective of claim 9, wherein incident rays on the
objective from a light source have a wavelength equal to of less
than 450 nm.
15. The objective of claim 10, wherein the thickness t is equal to
or greater than the focal length f.
16. The objective of claim 10, wherein the objective has an image
magnification of 0.
17. The objective of claim 10, wherein incident rays on the
objective from a light source have a wavelength equal to of less
than 450 nm.
18. The objective of claim 11, wherein the thickness t is equal to
or greater than the focal length f.
19. The objective of claim 11, wherein the objective has an image
magnification of 0.
20. The objective of claim 11, wherein incident rays on the
objective from a light source have a wavelength equal to of less
than 450 nm.
21. An optical pickup comprising: the objective of claim 9; a laser
source; and a photodetector.
22. An optical pickup comprising: the objective of claim 10; a
laser source; and a photodetector.
23. An optical pickup comprising: the objective of claim 11; a
laser source; and a photodetector.
24. The optical pickup of claim 21, wherein a working distance of
the objective depends on the diameter of an optical disk irradiated
with a laser beam emitted from the laser source and is defined as
follows:working distance>0.005.times.optical disk radius
25. The optical pickup of claim 22, wherein a working distance of
the objective depends on the diameter of an optical disk irradiated
with a laser beam emitted from the laser source and is defined as
follows:working distance>0.005.times.optical disk radius
26. The optical pickup of claim 23, wherein a working distance of
the objective depends on the diameter of an optical disk irradiated
with a laser beam emitted from the laser source and is defined as
follows:working distance>0.005.times.optical disk radius
27. An optical disk writer-reader comprising: the optical pickup of
claim 21; and a write-read unit to write and read information to
and from an optical disk through the pickup.
28. An optical disk writer-reader comprising: the optical pickup of
claim 22; and a write-read unit to write and read information to
and from an optical disk through the pickup.
29. An optical disk writer-reader comprising: the optical pickup of
claim 23; and a write-read unit to write and read information to
and from an optical disk through the pickup.
30. An optical disk reader comprising: the optical pickup of claim
21; and a read unit to read information from an optical disk
through the optical pickup.
31. An optical disk reader comprising: the optical pickup of claim
22; and a read unit to read information from an optical disk
through the optical pickup.
32. An optical disk reader comprising: the optical pickup of claim
23; and a read unit to read information from an optical disk
through the optical pickup.
Description
BACKGROUND OF THE INVENTION
[0001] 1. Field of the Invention
[0002] The present invention relates to an objective having a high
numerical aperture (NA) to realize a large-capacity optical disk,
an optical pickup with the objective, an optical disk writer-reader
with the objective, and an optical disk reader with the
objective.
[0003] 2. Description of the Related Art
[0004] Conventional objectives for compact disks (CDs) have
numerical apertures (NAs) of 0.45 to 0.5 and employ laser beams of
about 780 nm in wavelength to read and write the CDs. Objectives
for digital versatile disks (DVDs) have NAs of about 0.6 and employ
laser beams of about 650 nm in wavelength to read and write the
DVDs.
[0005] To handle high-capacity optical disks, now being developed
are next-generation pickups with objectives that have high NAs and
operate on short-wavelength beams.
[0006] The short wavelength beams may include a blue laser beam of
about 400 nm in wavelength.
[0007] Examples of objectives having high NAs are reported in the
following papers:
[0008] (A) Jpn. J. Appl. Phys. Vol. 39 (2000) pp. 978-979, M.
Itonaga et al. "Optical Disk System Using High-Numerical Aperture
Single Objective and Blue LD"
[0009] (B) Jpn. J. Appl. Phys. Vol. 39 (2000) pp. 937-942, I.
Ichimura et al. "Optical Disk Recording Using a GaN Blue-Violet
Laser Diode"
[0010] The paper (A) reports a system employing a single lens
having a numerical aperture of 0.7 and the paper (B) a system
employing two lens groups having a numerical aperture of 0.85.
[0011] Higher numerical apertures result in lowering system
margins. To cope with this problem, the systems reported in the
above papers further thin a CD transmission layer of 1.2 mm and a
DVD transmission layer of 0.6 mm. The paper (A) mentions a
thickness of 0.12 mm and the paper (B) a thickness of 0.1 mm.
Although the thickness of a transmission layer of an optical disk
depends on system margins, it is preferable to be about 0.3 mm or
thinner.
[0012] The two-lens-group system reported in the paper (B) realizes
a greater numerical aperture than the system of the paper (A). The
system of the paper (B), however, needs an assembling process of
two lens groups, and therefore, is disadvantageous to mass
production and increases costs.
[0013] According to the paper (B), the two-lens-group system
involves a working distance of about 0.13 mm, which is shorter than
about 1 mm of a single-lens system in a conventional DVD system.
The short working distance increases a risk of colliding with an
optical disk, thereby deteriorating the reliability of the
system.
[0014] Next-generation optical disk systems are required to have
single objectives having numerical apertures of 0.7 or above.
[0015] It is possible to design lenses having high numerical
apertures. Shotaro Yoshida details a method of designing a
double-sided aspherical lens having a high numerical aperture in
"Study in Aspherical Aplanatic Lens with Particularly Large
Aperture Ratio" in Tohoku University Institute of Scientific
Measurements Report, March, 1958.
[0016] Also, Japanese Patent Laid Open Publication 4-163510
discloses a single objective having a numerical aperture of about
0.6 to 0.8.
[0017] A lens having a high numerical aperture can be designed but
is not always manufacturable. For actual manufacturing, a designed
lens must secure a manufacturing tolerance. In addition, the
designed lens must be less affected by wavelength variations or
wavelength width of source light, to decrease chromatic
aberration.
[0018] A critical manufacturing tolerance for a double-sided
aspherical lens for an optical disk is a surface-to-surface
eccentricity tolerance. In addition to keeping the eccentricity
tolerance, the lens must simultaneously satisfy requirements for
axial aberration related to perpendicular incident light and
off-axis aberration related to oblique incident light.
[0019] It is nearly impossible for a lens having a numerical
aperture of 0.75 or higher to simultaneously satisfy these
requirements.
[0020] In a double-sided aspherical lens, off-axis aberration
worsens in proportion to an increase in the numerical aperture of
the lens even if no consideration is made on the manufacturing
tolerance of the lens. If the manufacturing tolerance is
considered, the off-axis aberration worsens because the
manufacturing tolerance, i.e., the eccentricity tolerance of the
lens is securable only by sacrificing the axial aberration and
off-axis aberration of the lens.
[0021] Although the axial aberration of the lens does not greatly
worsen with the consideration of the eccentricity tolerance, the
off-axis aberration of the lens greatly worsens when the numerical
aperture of the lens is higher than 0.6 and when the eccentricity
tolerance is of the micrometer order.
[0022] Chromatic aberration is usually put behind the manufacturing
tolerance. Namely, the manufacturing tolerance of a lens is
considered at first, and then, the shape of the lens is improved as
high as possible to minimize the chromatic aberration of the
lens.
[0023] Many studies have been made on the shapes of double-sided
aspherical lenses to improve lens performance. Some of the studies
are disclosed in Japanese Patent Laid Open Publications 5-241069
and 4-163510.
[0024] The publication 4-163510 discloses a range of lens shapes to
ensure good performance. This disclosure mentions nothing about the
securing of eccentricity tolerance. A second embodiment of the
disclosure explains a lens whose numerical aperture is greater than
0.75 (0.8 for a wavelength of 532 nm). This lens causes a large
aberration even on a slight eccentricity. The disclosure mentions
nothing about chromatic aberration.
[0025] The disclosures cover a wide range of specifications, and
therefore, are insufficient to actually design a good lens.
[0026] The two-lens-group system mentioned above involves a short
working distance, and therefore, greatly increases a risk of
colliding with an optical disk when the lens groups employ a higher
numerical aperture. Optical disks are generally made of plastic,
which unavoidably involves warp. A CD involves a warp of about 0.6
mm and a DVD involves a warp of about 0.3 mm, which is a double
improvement from the CD. No further improvement is expected in
optical disk warp because the warp depends on disk material. The
two-lens-group system has a working distance of 0.13 mm as
mentioned above. This working distance may differ depending on lens
design but must not be increased greater than 0.2 mm, to make a
pickup that employs the two-lens-group system compact. With such a
short working distance, the lens system will collide with an
optical disk if focus servo runs off due to disturbance, vibration,
or defects during a disk write or read operation.
[0027] There is another paper (C) Jpn. J. Appl. Phys. Vol. 41
(2002) pp. 1804-1807, G. Hashimoto et al. "Miniature Two-Axis
Actuator for High-Data-Transfer-Rate Optical Storage System." The
paper (C) discloses a compact system of two lens groups having a
numerical aperture of 0.85 and a focal distance of 0.88 mm. This
system may realize a compact actuator or pickup operating at high
speed. The system, however, involves a very short working distance
of 0.1 mm to increase a risk of collision.
SUMMARY OF THE INVENTION
[0028] An object of the present invention is to provide an
objective (objective lens or lens) for an optical disk, made of a
double-sided aspherical single lens (singlet) having a numerical
aperture equal to or greater than 0.75 and capable of minimizing
axial aberration, off-axis aberration, surface-to-surface
eccentricity aberration, and chromatic aberration. Also provided
are an optical pickup, an optical disk writer-reader, and an
optical disk reader each employing the objective.
[0029] An aspect of the present invention provides an objective for
an optical disk, wherein the objective has first and second
aspherical surfaces, a numerical aperture (NA) of the objective is
equal to or greater than 0.75 and a radius of curvature R1 of the
vertex of the first surface is defined as follows:
(1-D)A<R1<(1+D)A,
A=B/C,
B=0.85f(n-1) and
C=n(0.60866-0.11.multidot.t/f-0.1272.multidot.d/f)(0.83+0.2.multidot.NA)
[0030] where n is a refractive index of the lens, f is a focal
length of the lens, t is a thickness along optical axis through the
center of the lens, d is the thickness of a transmission layer of
the optical disk, and D is a positive number of 0.05, desirably
0.04, more desirably 0.03.
[0031] Desirably, another aspect of the present invention provides
an objective for an optical disk, wherein the objective has first
and second aspherical surfaces, a numerical aperture (NA) of the
objective is equal to of greater than 0.75 and an angle u1' between
a highest ray passing through the lens and an optical axis
satisfies the following condition:
(1-D)K<sin(u1')<(1+D)K and
K=(0.60866-0.11.multidot.t/f-0.1272.multidot.d/f)(0.83+0.2.multidot.NA).mu-
ltidot.NA/0.85
[0032] where f is a focal length of the lens, t is a thickness
along optical axis through the center of the lens, d is the
thickness of a transmission layer of the optical disk, and D is a
positive number of 0.06, desirably 0.05, more desirably 0.04.
[0033] Desirably, the highest ray entering the first surface of the
lens is parallel to the optical axis.
[0034] Desirably, the objective of any one of the above aspects has
a manufacturable eccentricity tolerance between the first and
second surfaces and minimizes off-axis aberration.
[0035] Desirably, still another aspect of the present invention
provides an objective for an optical disk, wherein the objective
has first and second aspherical surfaces, a numerical aperture (NA)
of the objective is equal to or greater than 0.75 and an angle
between a normal to the first surface at a point where a highest
ray enters and an optical axis is smaller than a predetermined
angle. Desirably, the predetermined angle is, for example, 57
degrees, desirably 56 degrees, more desirably 55 degrees.
[0036] Desirably, still another aspect of the present invention
provides an objective for an optical disk, wherein the objective
has first and second aspherical surfaces, numerical aperture (NA)
of the objective is equal to or greater than 0.75 and an angle
.theta. between a normal to the first surface at a point where a
highest ray enters and an optical axis satisfies the following
condition:
.theta.<.alpha.-47.3 (0.85-NA)(degrees)
[0037] where .alpha. is an angle of 57 degrees, desirably 56
degrees, more desirably 55 degrees.
[0038] Desirably, in the objective of any one of the above aspects,
the thickness t along optical axis through center of the objective
and focal length f satisfy the following condition:
t>(1+E)f
[0039] where E is a number equal to or greater than 0, desirably
0.1, more desirably 0.2.
[0040] Desirably, the objective of any one of the above aspects may
have an image magnification of 0. Namely, the lens desirably
focuses parallel rays if the lens involves no manufacturing errors
and if a wavelength of source light agrees with a reference
wavelength.
[0041] Desirably, the objective of any one of the above aspects may
be designed for source light of 450 nm or shorter in
wavelength.
[0042] Desirably, the objective of any one of the above aspects
properly operates on an optical disk having a transmission layer
thinner than 0.4 mm, i.e., thinner than a DVD's or CD's
transmission layer.
[0043] Desirably, the focal length f of the objective of any one of
the above aspects may be 10 mm or shorter, desirably 3.5 mm or
shorter.
[0044] The size (diameter) .phi. of a light flux that enters the
objective of any one of the above aspects depends on the numerical
aperture NA and focal length f of the lens and is expressed as
follows:
.phi.=2.times.NA.times.f
[0045] If the focal length is 10 mm and NA is 0.75, .phi.=15 mm.
This diameter is large relative to a light flux of about 5 mm or
smaller employed by many optical pickups. It is desirable,
therefore, that the focal length is shorter than 10 mm. If .phi.=5
mm and NA=0.75, then f=3.33 mm. It is more desirable that the focal
length is shorter than 3.5 mm.
[0046] The focal length of the objective of any one of the above
aspects is desirably 0 or greater, more desirably 0.2 mm or
greater.
[0047] Desirably, a working distance of the objective depends on
the thickness of an optical disk. Desirably, the thinner the
optical disk, the larger the working distance. Desirably, if there
is a very thin optical disk, a very small lens having a short focal
length will sufficiently work on the disk with a very short working
distance. Desirably, to work on a front-read optical disk, an
objective with a focal length of 0.1 mm may be designed. In this
case, a minimum focal length of the objective is desirably defined
as f>0. However, there is no means at present to manufacture
such a very small lens. Desirably, a practical minimum for the
focal length of an objective is f>0.2 mm.
[0048] Desirably, an upper limit of the thickness t of the
objective of any one of the above aspects is determined to make a
working distance "dw" of the lens positive. Desirably, the working
distance dw is defined as follows:
dw=fb-d/n'
[0049] where d is the thickness of an optical disk, n' is a
refractive index of the optical disk, and fb is defined as
follows:
fb=f(1-t(n-1)/n/R1)
[0050] where R1 is the radius of curvature of the first surface
mentioned above.
[0051] Desirably, as the lens thickness increases, the working
distance becomes shorter. Desirably, to provide a proper lens, a
finite working distance must be secured. Namely, an upper limit of
lens thickness desirably must be in a range where a finite working
distance is securable. Desirably, this range is determined by the
focal length and thickness of a lens and the thickness of an
optical disk.
[0052] Desirably, the lens thickness may be in the range of 1.5 mm
to 3.5 mm.
[0053] Desirably, the objective of any one of the above aspects is
applicable to an optical pickup. The optical pickup employing the
objective irradiates a track on an optical disk with a light flux
focused by the objective, to write and read information signals to
and from the optical disk. Desirably, the optical pickup may have
an image magnification of 0.
[0054] Desirably, still another aspect of the present invention
provides an optical pickup including the objective of any one of
the above aspects, a laser source, and a photodetector.
[0055] Desirably, a working distance of the objective of the
optical pickup dependens on the diameter of an optical disk
irradiated with a laser beam emitted from the laser source and is
defined as follows:
(working distance)>0.005.times.(optical disk radius)
[0056] Desirably, still another aspect of the present invention
provides an optical disk writer-reader including the optical pickup
of the above aspect and a write-read unit to write and read
information to and from an optical disk through the pickup.
[0057] Desirably, still another aspect of the present invention
provides an optical disk reader including the optical pickup of the
above aspect and a read unit to read information from an optical
disk through the optical pickup.
BRIEF DESCRIPTION OF THE DRAWINGS
[0058] FIG. 1 shows the structure of an objective;
[0059] FIG. 2 shows an angle of a ray in the lens of FIG. 1 and an
image magnification of a second surface of the lens;
[0060] FIG. 3 is a graph showing relationships between lens
thickness and angle u1 obtained from a regression formula and
design values;
[0061] FIG. 4 is a graph showing relationships between disk
thickness and angle u1 obtained from a regression formula and
design values;
[0062] FIG. 5 is a graph showing relationships between numerical
aperture (NA) and image magnification .beta.' obtained from a
regression formula and design values;
[0063] FIGS. 6A to 6C show the finding of a relational formula of
R1 and .beta.';
[0064] FIG. 7 is a graph showing a relationship between lens
thickness along optical axis through the center of a lens and
residual aberration due to a wavelength error of 5 nm;
[0065] FIG. 8 is a graph showing a relationship between lens
thickness and axial chromatic aberration (or back focal length fb)
with a lens having a focal length of 2 mm and a refractive index of
1.75 that is changed to 1.7486;
[0066] FIG. 9 is a sectional view showing an objective according to
an embodiment 1 of the present invention;
[0067] FIG. 10 is a graph showing a longitudinal aberration of the
objective of the embodiment 1;
[0068] FIG. 11 is a graph showing an offense against the sine
condition of the objective of the embodiment 1;
[0069] FIG. 12 is a graph showing an astigmatism of the objective
of the embodiment 1;
[0070] FIG. 13 is a graph showing relationships between R1 (radius
of curvature) and wavefront aberration of a lens having the same
refractive index and thickness as those of the lens of the
embodiment 1 and a slightly different R1;
[0071] FIG. 14 is a sectional view showing an objective according
to an embodiment 2 of the present invention;
[0072] FIG. 15 is a graph showing a longitudinal aberration of the
objective of the embodiment 2;
[0073] FIG. 16 is a graph showing an offense against the sine
condition of the objective of the embodiment 2;
[0074] FIG. 17 is a graph showing an astigmatism of the objective
of the embodiment 2;
[0075] FIG. 18 is a sectional view showing an objective according
to an embodiment 3 of the present invention;
[0076] FIG. 19 is a graph showing a longitudinal aberration of the
objective of the embodiment 3;
[0077] FIG. 20 is a graph showing an offense against the sine
condition of the objective of the embodiment 3;
[0078] FIG. 21 is a graph showing an astigmatism of the objective
of the embodiment 3;
[0079] FIG. 22 shows the geometries of a lens;
[0080] FIGS. 23A and 23B are graphs showing relationships between
first-surface incident angle and aberration;
[0081] FIG. 24 is a graph showing relationships between numerical
aperture and first-surface incident angle according to design
values and regression formulas;
[0082] FIG. 25 is a sectional view showing an objective according
to an embodiment 4 of the present invention;
[0083] FIG. 26 is a graph showing a longitudinal aberration of the
objective of the embodiment 4;
[0084] FIG. 27 is a graph showing an offense against the sine
condition of the objective of the embodiment 4;
[0085] FIG. 28 is a graph showing an astigmatism of the objective
of the embodiment 4;
[0086] FIG. 29 is a sectional view showing an objective according
to an embodiment 5 of the present invention;
[0087] FIG. 30 is a graph showing a longitudinal aberration of the
objective of the embodiment 5;
[0088] FIG. 31 is a graph showing an offense against the sine
condition of the objective of the embodiment 5;
[0089] FIG. 32 is a graph showing an astigmatism of the objective
of the embodiment 5;
[0090] FIG. 33 is a sectional view showing an objective according
to an embodiment 6 of the present invention;
[0091] FIG. 34 is a graph showing a longitudinal aberration of the
objective of the embodiment 6;
[0092] FIG. 35 is a graph showing an offense against the sine
condition of the objective of the embodiment 6;
[0093] FIG. 36 is a graph showing an astigmatism of the objective
of the embodiment 6;
[0094] FIG. 37 is a sectional view showing an objective according
to an embodiment 7 of the present invention;
[0095] FIG. 38 is a graph showing a longitudinal aberration of the
objective of the embodiment 7;
[0096] FIG. 39 is a graph showing an offense against the sine
condition of the objective of the embodiment 7;
[0097] FIG. 40 is a graph showing an astigmatism of the objective
of the embodiment 7;
[0098] FIG. 41 shows an optical pickup according to an embodiment 8
of the present invention; and
[0099] FIG. 42 is a block diagram showing an optical disk
writer-reader or an optical disk reader according to an embodiment
9 of the present invention.
DETAILED DESCRIPTION OF EMBODIMENTS
[0100] Objectives for optical disks, an optical pickup, an optical
disk writer-reader, and an optical disk reader according to
embodiments of the present invention will be described with
reference to the accompanying drawings.
[0101] Balancing axial aberration, off-axis aberration, and
eccentricity tolerance in designing an objective will be explained
first, and then, conditional formulas that define the objectives of
the present invention will be explained. The "eccentricity
tolerance" of a lens is definable based on a wavefront aberration
increase caused by eccentricity of the lens.
[0102] According to the present invention, the axial aberration,
off-axis aberration, and eccentricity tolerance of a lens are
secured by balancing the following three conditions:
[0103] (1) A spherical aberration of the lens must be corrected in
order to minimize the axial aberration;
[0104] (2) The lens must satisfy the sine condition in order to
minimize the off-axis aberration;
[0105] (3) The second surface of the lens must solely satisfy the
sine condition in order to secure a given eccentricity
tolerance.
[0106] In addition, chromatic aberration of the lens must be
secured by satisfying the following conditions:
[0107] (4) An aberration increase at the best focus of the lens for
each wavelength with respect to a wavelength error must be small,
wherein the aberration is referred to as spherical aberration
caused by a wavelength error;
[0108] (5) A focusing position change of the lens caused by a
wavelength error must be small in order to suppress an aberration
increase caused by wavelength spread of a light source.
[0109] The wavelength spread occurs when a semiconductor laser is
driven in a multimode by superimposing high frequencies to reduce
noise. Suppressing a focusing position change corresponds to
securing an axial chromatic aberration.
[0110] Basics of securing the axial aberration and off-axis
aberration of a lens will be explained, and then, the structure of
a lens capable of securing chromatic aberration will be
explained.
[0111] A double-sided aspherical lens is capable of simultaneously
satisfying the conditions (1) and (2) to secure axial and off-axis
aberrations. Any lens capable of simultaneously satisfying the
conditions (1) and (2) is called an aplanat.
[0112] A lens satisfying the conditions (1) and (2) is generally
incapable of satisfying the condition (3) to secure an eccentricity
tolerance.
[0113] If a lens satisfies the condition (2) and substantially
satisfies the condition (3), the lens as a whole satisfies the sine
condition and the second surface of the lens substantially
satisfies the sine condition. As a result, the first surface of the
lens substantially satisfies the sine condition in connection with
a ray height and a refraction angle.
[0114] An embodiment of the present invention balances the
conditions (1) and (2) to secure axial and off-axis aberrations and
the condition (3) to secure an eccentricity tolerance and properly
adjusts the degree of satisfaction of the condition (3), thereby
realizing a lens that involves suppressed axial and off-axis
aberrations and secures an eccentricity tolerance to actually
manufacture the lens.
[0115] The above-mentioned paper "Study in Aspherical Aplanatic
Lens with Particularly Large Aperture Ratio" (Shotaro Yoshida,
Tohoku University Institute of Scientific Measurements Report,
March, 1958) clarifies that a double-sided aspherical lens that
simultaneously satisfies the conditions (1) and (2) is obtainable
in a relatively wide range of vertex radiuses with a fixed focal
length and a lens radius changed by bending.
[0116] According to Yasuhiro Tanaka's "Aplanatic Single Lens
Designing and Application to Disk Optical System," Optics, 27, 12
(1998), p. 720, a lens that causes little surface-to-surface
eccentricity satisfies the condition (3).
[0117] It can be said that an aspherical lens that satisfies the
conditions (1) and (2) and conforms to the condition (3) has a
proper eccentricity tolerance. As mentioned above, it is unable to
simultaneously completely satisfy the conditions (1) to (3) because
a double-sided aspherical lens has design freedom only in two
aspherical surfaces in dealing with the three conditions (1) to
(3).
[0118] According to an analysis by the present inventor, the higher
the numerical aperture of a lens, the more the conditions (1) to
(3) become unsatisfied by the lens.
[0119] Conventional lenses for DVDs have a numerical aperture of
0.6 and those for CDs have a numerical aperture of 0.45. These
lenses having low numerical apertures cause only a little
aberration increase even when a vertex radius is widely changed,
and therefore, it is easy for such lenses to balance axial and
off-axis aberrations. Namely, the lenses may achieve a large
eccentricity tolerance for any vertex radius only by slightly
sacrificing the axial or off-axis aberration of the lenses.
[0120] On the other hand, a lens having a high numerical aperture
and operating on a short wavelength causes larger aberration
because aberration increases in inverse proportion to wavelength.
Such a lens, therefore, has a smaller design margin and must have a
strictly controlled shape (paraxial shape).
[0121] The present inventor found that a ray entering a lens at a
given height forms a given angle in the lens relative to an optical
axis irrespective of the refractive index of the lens, if the lens
has a predetermined focal length and a predetermined thickness and
works on an optical disk having a predetermined thickness. The
present inventor also found that the given angle mentioned above
depends on the thicknesses of the optical disk and lens.
[0122] Based on these lens characteristics found by the inventor,
lenses according to embodiments of the present invention properly
balance and secure the conditions (1) to (3).
[0123] FIG. 1 shows the structure of an objective for an optical
disk.
[0124] The objective 11 receives a light flux L1 from a light
source (not shown), refracts the light flux L1, and focuses the
light flux L1 on a recording plane of the optical disk 21. The
vertex of a first surface 1 of the lens 11 has a radius of
curvature R1, and the vertex of a second surface 2 of the lens 11
has a radius of curvature R2. The lens 11 has a thickness t along
optical axis through the center of the lens. The optical disk 21
has a transmission layer whose thickness is d. The lens 11 has a
working distance DW.
[0125] FIG. 2 shows a ray angle in the lens 11 and an image
magnification of the second surface 2.
[0126] In the light flux L1 that enters the lens 11 in parallel, a
highest ray is refracted by the first surface 1 of the lens 11 and
forms an angle u1 relative to an optical axis. The ray is further
refracted by the second surface 2 of the lens 11, to form an angle
u2 relative to the optical axis.
[0127] If the lens 11 has a numerical aperture of 0.85, the angle
u1 is expressed as follows:
sin(u1)=0.60866-0.11t/f-0.1272d/f (6)
[0128] The angle u1 in the formula (6) formed between the highest
ray refracted by the first surface 1 and the optical axis is also
formed by an aspheric aplanat having a numerical aperture of 0.85
and satisfying the conditions (1) and (2). This angle is determined
by the focal length f and thickness t along optical axis through
the center of the lens and the optical disk thickness d and is
irrelevant to the refractive index of the lens, if the lens has
proper characteristics.
[0129] FIG. 3 is a graph showing relationships between lens
thickness and angle u1 obtained from a regression formula and
design values. In FIG. 3, a black rhombus indicates a design value
and a straight line represents the regression formula.
[0130] The design values are calculated based on a focal length f
of 2 mm, a lens material refractive index n of 1.75, an optical
disk transmission layer thickness d of 0.1 mm, and different lens
thicknesses t. The design values well agree with the regression
formula, to show the correctness of the regression formula.
[0131] FIG. 4 is a graph showing relationships between disk
thickness and angle u1 obtained from a regression formula and
design values. In FIG. 4, a black rhombus indicates a design value
and a straight line represents the regression formula.
[0132] The design values are based on a focal length f of 2 mm, a
lens material refractive index n of 1.75, a lens thickness t of 3
mm, and different optical disk transmission layer thicknesses d.
The design values well agree with the regression formula, to show
the correctness of the regression formula.
[0133] To determine various constants for a lens according to the
formula (6), a paraxial formula will be employed.
[0134] In FIG. 2, each of the first and second surfaces of the lens
substantially satisfies the sine condition. A relationship between
the angles u1 and u2 is determined by an image forming operation on
the second surface. When a lens surface alone satisfies the sine
condition, an image magnification of actual rays on the lens
surface is constant and is equal to a paraxial magnification
irrespective of ray heights.
[0135] In this case, a paraxial image magnification .beta. on the
second surface of the lens is expressed as follows:
.beta.=n.multidot.up1/up2=n.multidot.sin(u1)/sin(u2)
[0136] where up1 and up2 are the inclinations of a paraxial ray and
u1 and u2 are the inclinations of an actual ray. A numerical
aperture for a highest ray, i.e., sin(u2) is 0.85, and therefore,
the following is obtained:
.beta.=n.multidot.sin(u1)/0.85
[0137] The present inventor found that u1 (up1 and .beta.) changes
according to numerical apertures.
[0138] This is because a lens that satisfies the conditions (1) and
(2) may involve a slight error in the condition (3). In this case,
the lens may be designed to satisfy the condition (3) at the
periphery of the lens where an angle of refraction becomes a
maximum. This will minimize the eccentricity of the lens. In this
way, the paraxial image magnification .beta. on the second surface
depends on numerical apertures.
[0139] The paraxial image magnification .beta. on the second
surface can be generalized by considering numerical apertures. A
generalized paraxial image magnification .beta.' on the second
surface of a lens with a numerical aperture of NA is expressed as
follows:
.beta.'=.beta.(0.83+0.2.multidot.NA)
[0140] FIG. 5 is a graph showing relationships between numerical
aperture (NA) and image magnification .beta.' obtained from a
regression formula and design values. In FIG. 5, a black rhombus
indicates a design value and a straight line represents the
regression formula.
[0141] The design values are based on a focal length f of 2 mm, a
lens material refractive index n of 1.75, a lens thickness t of 2
mm, and different numerical apertures. The design values well agree
with the regression formula, to show the correctness of the
regression formula.
[0142] A radius of curvature R1 of the first surface of a lens and
a generalized paraxial image magnification .beta.' on the second
surface of the lens have the following relationship:
R1=f(n-1)/.beta.'
[0143] FIGS. 6A to 6C show the finding of this formula.
[0144] In FIG. 6A, a lens 111 has a refractive index n. A first
surface 101 of the lens 111 has a radius of curvature R101, and a
second surface 102 thereof has an infinite radius of curvature
R102. A ray L101 entering the lens 111 is in parallel with an
optical axis. The second surface 102 is flat because the radius of
curvature R102 is infinite. A focal length f' of the lens 111, the
radius of curvature R101, and the refractive index n are expressed
as follows:
f'=R/(n-1)
[0145] In FIG. 6B, an image plane (image space) 112 has a
refractive index n. A ray L101 is in parallel with an optical axis
and enters a first surface 101 having a radius of curvature R101.
The ray L101 intersects the optical axis at a distance L from the
vertex of the first surface 101. In this case, the following
relationship is established:
f'=L/n
[0146] Accordingly, the radius of curvature R101 of the first
surface 101 is expressed as follows:
R101=(n-1)f'=(n-1)/n.multidot.L
[0147] FIG. 6C is an expansion to a double convex lens. The double
convex lens 113 receives a ray having a maximum height h in
parallel with an optical axis. A length L in FIG. 6C corresponds to
the length L in FIG. 6B. According to the definition of a
magnification, the following is obtained:
.beta.=n.multidot.u1/u2=n.multidot.f/L
[0148] This can be written as follows:
L=n.multidot.f/.beta.
[0149] Based on this, the radius of curvature R101 of the first
surface 101 can be expressed with the refractive index n, focal
length f, and image magnification .beta. as follows:
R101=(n-1).multidot.f/.beta.
[0150] Consequently, the before-mentioned formula for R1 and
.beta.' is obtained. Based on the formula, R1 is obtained as
follows:
R1=B/C
B=0.85f(n-1)
C=n(0.60866-0.11.multidot.t/f-0.1272.multidot.d/f)(0.83+0.2.multidot.NA)
[0151] A lens having a numerical aperture equal to of greater than
0.75 and a sufficient eccentricity tolerance may be designed with
the radius R1 of curvature involving a deviation ratio of 0.05,
preferably 0.04, more preferably 0.03 or smaller from the value R1
in the above formula.
[0152] Sin(u1) is in inverse proportion to R1. Due to the
characteristics of the sin function, a change in sin(u1) is
relatively small compared to a change in u1, and therefore, a
change in R1 results in a large change in u1. Namely, a tolerance
for u1 is greater than a tolerance for R1.
[0153] According to these facts, conditions for a radius of
curvature R1 of the first surface of a lens are summarized as
follows:
(1-D)A<R1<(1+D)A (7)
A=B/C
B=0.85f(n-1)
C=n(0.60866-0.11.multidot.t/f-0.1272.multidot.d/f)(0.83+0.2.multidot.NA)
[0154] where D is a positive number, which is 0.05, preferably
0.04, more preferably 0.03. The value D may be any number in the
range of 0.03 to 0.05.
[0155] The influence of the optical disk transmission layer is
relatively small if the refractive index of the transmission layer
is in the range of 1.45 to 1.65.
[0156] The range of 0.03 to 0.05 for the positive number D is set
to cover variations in the refractive index of the optical disk,
more precisely, variations in the refractive index of the lens.
[0157] If the refractive index of the lens is low and if the
numerical aperture of the lens is smaller than 0.75, the margin
will increase. In this case, the range for the positive number D
may be increased by 5%, to design a proper lens.
[0158] A lens satisfying the condition (7) relating to the radius
of curvature R1 of the first surface of the lens simultaneously
satisfies the requirements for the axial aberration, off-axis
aberration, and eccentricity tolerance of the lens.
[0159] An aspherical lens according to an embodiment of the present
invention may be a lens having a rotational symmetry shape around
an optical axis (coaxial optical system), or a toric lens having
slightly different aspherical shapes in different directions. The
radius of curvature R1 in each direction of the first surface of
the toric lens must be within the above-mentioned range.
[0160] Once a radius of curvature R1 of the first surface of a lens
is set according to the condition (7), a radius of curvature R2 of
the second surface of the lens is automatically determined from a
focal length f of the lens as follows:
R2=G/H
G=f(n-1)(t(n-1)/n-R1)
H=(R1-f(n-1))
[0161] This formula is easily obtained from a basic formula to
calculate a paraxial focal length of a single lens according to the
radiuses of both surfaces and thickness of the lens.
[0162] In this way, the radius of curvature R1 at the vertex of the
first surface of a lens, and the radius of curvature R2 at the
vertex of the second surface of the lens are determined. According
to the radiuses of curvature R1 and R2 and the conditions (1) and
(2), the shapes of the aspherical surfaces of the lens are uniquely
determined. At this time, the lens well satisfies the sine
condition of the condition (3), to provide a large eccentricity
tolerance.
[0163] As explained above, it is impossible to satisfy the
condition (3) while completely satisfying the conditions (1) and
(2). This is because an aspherical lens has design freedom only on
two aspherical surfaces with respect to the three conditions.
Namely, an aspherical lens has a design freedom of 2. However it is
possible to increase an eccentricity tolerance by slightly changing
the aspherical shapes completely satisfying the conditions (1) and
(2) as mentioned above. This unavoidably results in deteriorating
the axial aberration and off-axis aberration of the lens, but can
secure or allow a manufacturing tolerance greater than order of
micrometer for example that is important to practically produce the
lens.
[0164] In other words, the present invention properly deteriorates
the axial aberration and off-axis aberration of a lens, thereby
balancing the characteristics of the lens and securing an
eccentricity tolerance for the lens. Namely, the present invention
properly adjusts the satisfaction levels of the conditions (1) to
(3) when designing a lens. In the present embodiment, the
conditions (1) to (3) are simultaneously satisfied to some extent
by deteriorating the conditions (1) and (2) while securing
condition (3). This balancing secures the eccentricity tolerance
greater than the order of micrometers for example.
[0165] To find proper aspherical shapes for a lens, the spherical
radiuses of the lens must meet the conditions (6) and (7).
Otherwise, the lens is unable to secure a proper eccentricity
tolerance and may involve imbalanced axial aberration and off-axis
aberration.
[0166] The above mentioned lens securing an eccentricity tolerance
dose not satisfy a sufficient condition securing a chromatic
aberration because the conditions (4) and (5) are not considered.
The chromatic aberration will be explained in detail hereafter.
[0167] To improve the satisfaction levels of the conditions (4) and
(5) for a lens, the thickness t along optical axis through the
center of a lens and focal length f of the lens must satisfy the
following condition:
t>(1+E)f
[0168] where E is a number equal to or larger than 0, preferably 0,
more preferably 0.1, still more preferably 0.2.
[0169] According to the condition (4), an aberration increase at
the best focus of a lens at each wavelength must be small with
respect to a wavelength error. As the thickness along optical axis
through the center of a lens becomes thicker, the radius of the
first surface (incident surface) of the lens becomes larger. More
precisely, as the radius of curvature of the first surface of a
lens increases, a ray entering the periphery of the lens makes a
smaller incident angle .theta. (an angle between a normal to the
first surface and the ray). This results in reducing a refraction
effect, which is a nonlinear phenomenon, and reducing spherical
aberration with respect to a wavelength change.
[0170] FIG. 7 is a graph showing a relationship between lens
thickness along optical axis through the center of a lens and
residual aberration due to a wavelength error of 5 nm. The residual
aberration is spherical aberration. This graph was prepared on many
designed lenses having an NA of 0.85, a focal length of 2.5 mm, and
lens material of Ohara LAM70. The lenses were designed with a
relatively large eccentricity tolerance.
[0171] According to the graph of FIG. 7, an aberration of
0.04.lambda. or greater occurs when the lens thickness becomes
thinner than the focal length. The aberration greatly increases
when the lens thickness is thinner than 3 mm, which is 1.2 times
the focal length.
[0172] According to the condition (5), an aberration increase
caused by wavelength spread of a light source must be small. If
there is a light source having wavelength spread, wavelengths
around a center wavelength produce focusing errors in addition to
the spherical aberration mentioned above when an observation plane
is set on a best image plane of the center wavelength. In practice,
the influence of the focusing errors is greater than that of
spherical aberration. For wavelengths shorter than 450 nm (0.45
.mu.m), the refractive index of glass greatly disperses to increase
the influence of the focusing errors.
[0173] A focusing error occurs due to a change in the back focal
length of a lens when a wavelength changes. The back focal length
fb of a lens is obtained from a ray tracing formula based on a
paraxial approximation as follows:
fb=f(1-t(n-1)/n/R1)
[0174] A change in the refractive index n of the lens due to glass
dispersion causes a change in the back focal length fb, and this
back focal length change is a focusing error.
[0175] FIG. 8 is a graph showing a relationship between lens
thickness and axial chromatic aberration (or back focal length fb)
measured in lenses having a focal length of 2 mm and a refractive
index changed from 1.75 to 1.7486. A change in the back focal
length fb of each lens corresponds to an axial chromatic
aberration. The refractive index change from 1.75 to 1.7486
corresponds to a refractive index change due to a wavelength change
of about 5 nm when glass having an Abbe number of about 45 is used
with a wavelength of around 400 nm. The lenses are each a
plano-convex lens having a radius of curvature R1 of 1.5 mm. Lenses
according to the present invention are not plano-convex lenses but
are double-sided spherical lenses, more precisely, double-sided
aspherical lenses. Paraxial values including f and fb of a lens are
determined by the radius of the vertex of the lens, and therefore,
a spherical lens and an aspherical lens make no difference between
them. A change in the back focal length fb of a spherical lens is
substantially free from the influence of bending of the lens, which
changes the radiuses of curvature R1 and R2 of the lens while
keeping the focal length of the lens, and is substantially equal to
that of a plano-convex lens. Accordingly, FIG. 8 is effective to
consider spherical lenses. According to the graph of FIG. 8, the
axial chromatic aberration becomes smaller in proportion to the
lens thickness. In this regard, the lens thickness must be as thick
as possible.
[0176] According to the formulas described in this specification, a
perfect aplanat has a first surface radius that minimizes an
eccentricity aberration increase. When balancing aberration
conditions as mentioned above, it is not always necessary to employ
a radius that realizes a minimum eccentricity aberration. Within
the conditional ranges specified by the formulas, a radius close to
the eccentricity aberration minimizing radius is employed as a
radius of the vertex of an aspheric shape of a given lens, to
balance the axial aberration and off-axis aberration of the
lens.
[0177] Balancing these aberration conditions is to consider design
freedom levels and is equal to introduce imperfection into a
perfect aplanat. According to an embodiment of the present
invention, the radiuses of a lens can be balanced by adding a
degree of freedom thereto.
[0178] If a radius of curvature of a lens is out of the conditions
specified by the present invention, aberrations of the lens will be
imbalanced. It is necessary, therefore, to keep the conditions.
[0179] In the above, a change in the characteristics of a lens due
to a numerical aperture change has been explained in connection
with a change in an image magnification .beta. of the lens. A
change in an angle u1 between a highest ray in a lens and an
optical axis will be explained in connection with a change in the
numerical aperture of the lens.
[0180] When the numerical aperture of a lens changes, the angle u1
changes substantially proportionally. Due to the reasons mentioned
in connection with a change in the image magnification .beta., a
change in the angle u1 is not strictly a proportional change. A
change in the angle u1 causes a change in the image magnification
.beta..
[0181] A lens having a numerical aperture including 0.85 forms an
angle u1' between a highest ray in the lens and an optical axis,
wherein the highest ray enters the first surface of the lens
parallel to the optical axis. The angle u1' is expressed as
follows:
sin(u1')=(0.60866-0.11.multidot.t/f-0.1272.multidot.d/f)(0.83+0.2.multidot-
.NA).multidot.NA/0.85
[0182] where f is a focal length of the lens, t is a thickness
along optical axis through the center of the lens, d is the
thickness of a transmission layer of an optical disk on which the
lens works, and NA is a numerical aperture of the lens.
[0183] To design a lens having a numerical aperture equal to or
greater than 0.75 and a sufficient eccentricity tolerance, the sine
of an angle u1' of the lens must keep a deviation ratio of 0.06,
preferably 0.05, more preferably 0.04 from K mentioned above.
[0184] This condition on the angle u1' is expressed as follows:
(1-D)K<sin(u1')<(1+D)K (8)
K=(0.60866-0.11.multidot.t/f-0.1272.multidot.d/f)(0.83+0.2.multidot.NA).mu-
ltidot.NA/0.85
[0185] where D is a positive number of 0.06, preferably 0.05, more
preferably 0.04. The number D may be any number in the range of
0.04 to 0.06.
[0186] The influence of a transmission layer of an optical disk is
relatively small if the refractive index of the transmission layer
is in the range of 1.45 to 1.65.
[0187] The range of 0.04 to 0.06 for the positive number D is to
cover different disk refractive indexes, more precisely, different
lens refractive indexes.
[0188] Lenses having numerical apertures of less than 0.75 have
greater margins, and therefore, the range for the positive number D
for such lenses may be expanded by 6%.
[0189] The thickness t along optical axis through the center of the
lens and focal length f of the lens satisfying the above condition
must satisfy the following condition:
t>(1+E)f
[0190] where E is a number equal to or greater than 0, preferably
0.1, more preferably 0.2.
[0191] In consequence, a lens that satisfies the condition (4) for
an angle u1' between a highest ray in the lens and an optical axis
can simultaneously satisfy requirements for axial aberration,
off-axis aberration, and an eccentricity tolerance.
[0192] An aspherical lens according to an embodiment of the present
invention may be a lens having a rotational symmetry shape around
an optical axis (coaxial optical system), or a toric lens having
slightly different aspherical shapes in different directions. A
radius of curvature in each direction of the first surface of the
toric lens and the thickness of the toric lens must be within the
above-mentioned ranges.
[0193] An optical pickup, an optical disk writer-reader; and an
optical disk reader each employing the lens of the present
invention will be explained.
[0194] A working distance of the lens must be greater than a
maximum face runout of an optical disk on which the lens works.
[0195] This is to prevent the lens from colliding with the disk
even if focus serve errs due to, for example, disk defects,
disturbance, or vibration. If no focus serve operates, a collision
avoiding measure such as moving the lens away from the disk will be
taken. Accordingly, a risk of collision is high when trouble occurs
during the focus serve.
[0196] If an optical disk warps in a simple bowl shape at a warp
angle of .alpha., a face runout quantity L of the disk at a radius
R is as follows:
L=R.multidot.tan(.alpha.)
[0197] Disk warp angles are specified in disk standards and are 0.6
degrees for CDs and 0.3 degrees for DVDs. A maximum face runout of
a disk occurs at the periphery thereof. Namely, a CD of 120 mm
diameter may have a face runout of 0.6 mm, and a DVD of 120 mm
diameter may have a face runout of 0.3 mm.
[0198] Even a high-density disk is made of plastic, and therefore,
it is difficult to reduce a warp of the disk. A maximum face runout
of a disk is proportional to a radius of the disk. Namely, a face
runout L of a disk having a maximum radius R on which an optical
pickup or an optical disk writer-reader operates is expressed as
follows:
L=0.005.multidot.R
[0199] A working distance dw of a lens is as follows:
dw=fb-d/nd
[0200] where d is the thickness of an optical disk, nd is the
refractive index of the optical disk, and fb is defined as
follows:
fb=f(1-t(n-1)/n/R1)
[0201] where R1 a radius of curvature of the lens.
[0202] As the thickness of a lens increases, the working distance
thereof becomes shorter. To provide a proper lens, the working
distance thereof must be finite. Namely, an upper limit of the
thickness of a lens must be in a range where the working distance
of the lens is finite. This range is determined by the focal length
and thickness of the lens and the thickness of an optical disk.
[0203] The lens thickness may be in the range of 2 mm to 3.5
mm.
[0204] It is preferable to make the working distance dw greater
than the maximum warp L of an optical disk as follows:
dw>L(=0.005.multidot.R)
[0205] If the maximum radius of a disk handled by an optical disk
writer-reader is 60 mm, the working distance is 0.3 mm or over. If
the maximum disk radius is 25 mm, the working distance is 0.125 mm
or over. If the maximum disk radius is 40 mm, the working distance
is 0.1 mm or over.
[0206] It is apparent from the above formula that the focal length
of a lens must be increased to allow the large working distance of
the lens. Elongating the focal length, however, increases the size
of the lens, thereby increasing the size of an optical pickup or an
optical disk writer-reader. A large lens is disadvantageous for the
frequency characteristics of a lens actuator and is unable to
realize a high transmission rate.
[0207] Namely, there is a preferable focal length range for a lens.
According to an embodiment of the present invention, the focal
length of a lens is preferably 10 mm or smaller, more preferably
3.5 mm or smaller.
[0208] The size (diameter) .phi. of a light flux entering a lens
depends on the numerical aperture (NA) and focal length f of the
lens and is expressed as follows:
.phi.=2.times.NA.times.f
[0209] If the focal length is 10 mm and NA is 0.75, .phi.=15 mm.
This light flux diameter is large compared with many optical
pickups that use a light flux diameter of 5 mm or smaller. It is
required, therefore, that the focal length of a lens be 10 mm or
smaller. If .phi.=5 mm and NA=0.75, f=3.33 mm. Namely, the focal
length of a lens is preferably 3.5 mm or below.
[0210] An optical pickup according to an embodiment of the present
invention employs the objective of any one of the embodiments of
the present invention. The optical pickup employing the objective
emits a focused light flux toward a track on an optical disk to
write and read information signals to and from the optical disk.
The optical pickup preferably has an image magnification of 0.
[0211] An optical disk writer-reader or an optical disk reader
according to an embodiment of the present invention employs the
objective of any one of the embodiments of the present invention.
The optical disk writer-reader or optical disk reader employing the
objective emits a focused light flux toward a track on an optical
disk to write and read information signals to and from the optical
disk. The optical disk writer-reader or optical disk reader
preferably has an image magnification of 0.
[0212] Objectives for optical disks according to embodiments of the
present invention will be explained.
[0213] In the following embodiments, an aspherical surface of a
lens is expressed with the following polynomial:
Z=CR.sup.2/(1+(1-(1+K)C.sup.2R.sup.2).sup.0.5)+AR.sup.4+BR.sup.6+CR.sup.8+-
DR.sup.10+ER.sup.12+FR.sup.14
[0214] where Z is a distance from the vertex of the surface, R is a
height from an optical axis, K is a conic constant, and A to F are
aspherical coefficients of degrees 4 to 14. For example, A is a
coefficient for R.sup.4.
[0215] Embodiment 1
[0216] FIG. 9 is a sectional view showing an objective according to
the embodiment 1 of the present invention. This lens is referred to
as the lens 11.sub.01.
[0217] A light flux L enters the lens 11.sub.01, is refracted by a
first surface 1 and a second surface 2 of the lens 11.sub.01, is
transmitted through a third surface 3 and transmission layer of an
optical disk 21, and is focused on a signal recording plane of the
optical disk 21.
[0218] Table 1 shows specifications of the lens 11.sub.01.
1 TABLE 1 Design wavelength 405 nm Numerical aperture 0.85 Focal
length 2 mm Entrance pupil diameter 3.4 mm Disk thickness 0.1 mm
Image magnification 0
[0219] Table 2 shows design values for the lens 11.sub.01. Units
for radiuses and thicknesses are mm in Table 2 and in other tables
that follow.
2TABLE 2 Surface Surface Thick- Refractive Conic No. shape Radius
ness Index constant 1 Aspheric 1.71 2.75 1.85 -0.9168291 2 Aspheric
-75.9027 0.4605 -- 2518.06 3 -- Infinite 0.1 1.62230752 -- Image --
-- -- -- -- surface
[0220] Table 3 shows aspherical coefficients for the first surface
of the lens 11.sub.01.
3 TABLE 3 Coefficient for R.sup.4 0.013687371 Coefficient for
R.sup.6 0.00087533585 Coefficient for R.sup.8 0.00087533585
Coefficient for R.sup.10 -0.00077467164 Coefficient for R.sup.12
0.00030433925 Coefficient for R.sup.14 -5.3502493 .times.
10.sup.-5
[0221] Table 4 shows aspherical coefficients for the second surface
of the lens 11.sub.01.
4 TABLE 4 Coefficient for R.sup.4 0.22363727 Coefficient for
R.sup.6 -0.58889528 Coefficient for R.sup.8 0.72567392 Coefficient
for R.sup.10 -0.47382503 Coefficient for R.sup.12 0.12985027
[0222] According to the lens specifications, a recommended value
for R1, or a value for A of the formula (7) is calculated as
1.731695 mm. From this recommended value, the design value for R1
deviates by 1.25%.
[0223] The lens 11.sub.01 is an aplanat that substantially
satisfies the conditions (1) and (2) and leaves little error in the
condition (3).
[0224] The lens 11.sub.01 involves an axial wavefront aberration of
0.002.lambda., which is very small and is substantially zero in
practical use. The lens shows a wavefront aberration of
0.023.lambda. for an incident ray of 0.5 degrees in off-axis angle.
This value is satisfactory. With respect to a surface-to-surface
eccentricity of 3 .mu.m, the lens shows a wavefront aberration of
0.036.lambda.. This aberration concerning the surface-to-surface
eccentricity is critical when manufacturing the lens, and the
aberration demonstrated by the lens 11.sub.01 is satisfactorily
small.
[0225] A working distance of the lens 11.sub.01 is 0.4605 mm, which
is larger than a preferable working distance of 0.3 mm for a disk
of 60 mm radius.
[0226] A highest ray to the lens 11.sub.01 forms an angle u1' in
the lens, and this angle provides sin(u1')=0.46. A recommended
value for sin(u1') calculated from the lens specifications, i.e., K
of the formula (8) is 0.4511. From this recommended value, the
design value deviates by 1.97%.
[0227] FIG. 10 is a graph showing a longitudinal aberration of the
lens 11.sub.01, FIG. 11 is a graph showing an offense against the
sine condition of the lens 11.sub.01, and FIG. 12 is a graph
showing an astigmatism of the lens 11.sub.01.
[0228] FIG. 13 is a graph showing relationships between R1 (radius
of curvature) and wavefront aberration of lenses having the same
refractive index and thickness as those of the lens 11.sub.01 and
slightly different radiuses of curvature R1. The lenses involve an
eccentricity of 3 .mu.m.
[0229] In FIG. 13, white squares represent lenses having a
numerical aperture of 0.75, and black rhombuses represent lenses
having a numerical aperture of 0.85. Curves plotting these marks
show aberration increases.
[0230] The value A of the formula (7) is 1.767 mm for the lenses
having a numerical aperture of 0.75, and 1.732 mm for the lenses
having a numerical aperture of 0.85.
[0231] From FIG. 13, it is understood that, if an eccentricity
aberration limit is set as 0.04.lambda., the radius of curvature R1
of the first surface of a lens must be set within 5% of the
recommended value A. Preferably, it must be set within 4% of the
recommended value, to secure an eccentricity aberration of
0.04.lambda. or below.
[0232] As the numerical aperture of a lens increases, aberration
relative to a change in R1 rises. In consideration of this, it is
preferable to set the radius of curvature R1 within 3% of the
recommended value A.
[0233] In the lenses having a numerical aperture of 0.85, the
radius of curvature R1 at a best aberration point deviates from the
theoretical value A by about 1%. This is because of an error in the
regression formula. The range mentioned above takes this error into
account.
[0234] According to the lens specifications, an eccentricity of 3
.mu.m causes an aberration of 0.04.lambda.. Other lens
specifications may provide relatively large aberration. Even in
such a case, the radius of curvature of a lens must be suppressed
within the above-mentioned range.
[0235] The thickness of the lens 11.sub.01 is 1.375 times the focal
length thereof. The lens 11.sub.01 is made of glass material having
a fixed refractive index. A wavelength change of 5 nm may change
the refractive index to 1.8486, to cause an aberration of
0.01.lambda. on a best image plane. This aberration is small. An
axial chromatic aberration is 2.17 .mu.m, which is also small.
[0236] Embodiment 2
[0237] FIG. 14 is a sectional view showing an objective according
to the embodiment 2 of the present invention. This lens is referred
to as the lens 11.sub.02.
[0238] A light flux L enters the lens 11.sub.02, is refracted by a
first surface 1 and a second surface 2 of the lens 11.sub.02, is
transmitted through a third surface 3 and transmission layer of an
optical disk 21, and is focused on a signal recording plane of the
optical disk 21.
[0239] Table 5 shows specifications of the lens 11.sub.02.
5 TABLE 5 Design wavelength 405 nm Numerical aperture 0.8 Focal
length 1.750 mm Entrance pupil diameter 2.8 mm Image magnification
0
[0240] Table 6 shows design values for the lens 11.sub.02.
6TABLE 6 Surface Surface Thick- Refractive Conic No. shape Radius
ness Index constant 1 Aspheric 1.45 2.5 1.75 -0.9753354 2 Aspheric
-3.613636 0.395 -- -- 3 -- Infinite 0.1 1.62230752 -188.2991 Image
-- -- -- -- -- surface
[0241] Table 7 shows aspherical coefficients for the first surface
of the lens 11.sub.02.
7 TABLE 7 Coefficient for R.sup.4 0.023305393 Coefficient for
R.sup.6 0.017039056 Coefficient for R.sup.8 0.0023431785
Coefficient for R.sup.10 -0.0023798936 Coefficient for R.sup.12
0.0013373117 Coefficient for R.sup.14 -0.00035090993
[0242] Table 8 shows aspherical coefficients for the second surface
of the lens 11.sub.02.
8 TABLE 8 Coefficient for R.sup.4 0.17601287 Coefficient for
R.sup.6 -0.54949768 Coefficient for R.sup.8 0.50420582 Coefficient
for R.sup.10 0.12942116 Coefficient for R.sup.12 -0.37309714
[0243] According to the lens specifications, a recommended value
for R1, or a value for A of the formula (7) is calculated as 1.4495
mm. From this recommended value, the design value deviates by 0.3%.
The lens 11.sub.02 is an aplanat that substantially satisfies the
conditions (1) and (2) and leaves little error in the condition
(3).
[0244] The lens 11.sub.02 involves an axial wavefront aberration of
0.001.lambda., which is very small and is substantially zero in
practical use. The lens shows a wavefront aberration of
0.013.lambda. for an incident ray of 0.5 degrees in off-axis angle.
This value is satisfactory. With respect to a surface-to-surface
eccentricity of 3 .mu.m, the lens shows a wavefront aberration of
0.023.lambda.. This aberration concerning the surface-to-surface
eccentricity is critical when manufacturing the lens, and the
aberration demonstrated by the lens 11.sub.02 is satisfactorily
small.
[0245] A working distance of the lens 11.sub.02 is 0.395 mm, which
is larger than a preferable working distance of 0.3 mm for a disk
of 60 mm radius.
[0246] A highest ray to the lens 11.sub.02 forms an angle u1' in
the lens, and this angle provides sin(u1')=0.421. A recommended
value for sin(u1') calculated from the lens specifications, i.e., K
of the formula (8) is 0.44. From this recommended value, the design
value deviates by 1.7%.
[0247] FIG. 15 is a graph showing a longitudinal aberration of the
lens 11.sub.02, FIG. 16 is a graph showing an offense against the
sine condition of the lens 11.sub.02, and FIG. 17 is a graph
showing an astigmatism of the lens 11.sub.02.
[0248] The thickness of the lens 11.sub.02 is 1.429 times the focal
length thereof. The lens 11.sub.02 is made of glass material having
a fixed refractive index. A wavelength change of 5 nm may change
the refractive index to 1.7486, to cause an aberration of
0.01.lambda. on a best image plane. This aberration is small. An
axial chromatic aberration is 2.10 .mu.m, which is also small.
[0249] Embodiment 3
[0250] FIG. 18 is a sectional view showing an objective according
to the embodiment 3 of the present invention. This lens is referred
to as the lens 11.sub.03.
[0251] A light flux L enters the lens 11.sub.03, is refracted by a
first surface 1 and a second surface 2 of the lens 11.sub.03, is
transmitted through a third surface 3 and transmission layer of an
optical disk 21, and is focused on a signal recording plane of the
optical disk 21.
[0252] Table 9 shows specifications of the lens 11.sub.03.
9 TABLE 9 Design wavelength 405 nm Numerical aperture 0.85 Focal
length 2.2 mm Entrance pupil diameter 3.74 mm Disk thickness 0.1 mm
Image magnification 0
[0253] Table 10 shows design values for the lens 11.sub.03.
10TABLE 10 Surface Surface Thick- Glass Conic No. shape Radius ness
material constant 1 Aspheric 1.812171 3.104 NBF1 -0.3371789 2
Aspheric -6.507584 0.500289 -- -845.6516 3 -- Infinite 0.1 Polycar-
-- bonate 4 Image -- -- -- -- surface
[0254] Table 11 shows aspherical coefficients for the first surface
of the lens 11.sub.03.
11 TABLE 11 Coefficient for R.sup.4 -0.00092006967 Coefficient for
R.sup.6 -0.00025706693 Coefficient for R.sup.8 -0.00057872391
Coefficient for R.sup.10 0.0002222827 Coefficient for R.sup.12
-5.6787923 .times. 10.sup.-5
[0255] Table 12 shows aspherical coefficients for the second
surface of the lens 11.sub.03.
12 TABLE 12 Coefficient for R.sup.4 0.061448774 Coefficient for
R.sup.6 -0.13995629 Coefficient for R.sup.8 0.12867014 Coefficient
for R.sup.10 -0.043733069
[0256] Table 13 shows refractive indexes of the glass
materials.
13 TABLE 13 NBF1 1.76775590 Polycarbonate 1.62031432
[0257] According to the lens specifications, a recommended value
for R1, or a value for A of the formula (7) is calculated as
1.81581 mm. From this recommended value, the design value deviates
by 0.2%. The lens 11.sub.03 is approximately an aplanat that
substantially satisfies the condition (1), is slightly
unsatisfactory for the condition (2) so that the lens 11.sub.03 may
suppress eccentricity aberration more than the lens 11.sub.01, and
leaves little error in the condition (3).
[0258] The lens 11.sub.03 involves an axial wavefront aberration of
0.006.lambda., which is very small and is substantially zero in
practical use. The lens shows a wavefront aberration of
0.069.lambda. for an incident ray of 0.5 degrees in off-axis angle.
This value is satisfactory. With respect to a surface-to-surface
eccentricity of 5 .mu.m, the lens shows a wavefront aberration of
0.034.lambda.. This aberration concerning the surface-to-surface
eccentricity is critical when manufacturing the lens, and the
aberration demonstrated by the lens 11.sub.03 is satisfactorily
small.
[0259] A highest ray to the lens 11.sub.03 forms an angle u1' in
the lens, and this angle provides sin(u1')=0.466. A recommended
value for sin(u1') calculated from the lens specifications, i.e., K
of the formula (8) is 0.464. From this recommended value, the
design value deviates by 0.43%.
[0260] FIG. 19 is a graph showing a longitudinal aberration of the
lens 11.sub.03, FIG. 20 is a graph showing an offense against the
sine condition of the lens 11.sub.03, and FIG. 21 is a graph
showing an astigmatism of the lens 11.sub.03.
[0261] The thickness of the lens 11.sub.03 is 1.411 times the focal
length thereof. A wavelength change of 5 nm to 410 nm may cause an
aberration of 0.029.lambda. on a best image plane. This aberration
is small. An axial chromatic aberration is 2.21 .mu.m, which is
also small.
[0262] The aspherical shape of the lens may slightly be changed to
increase the eccentricity tolerance. In this case, the axial
aberration or the off-axis aberration of the lens may deteriorate.
Increasing the eccentricity tolerance, i.e., providing a
sufficiently large manufacturing tolerance, however, is important
when practically design the lens.
[0263] Providing a lens with a sufficient eccentricity tolerance
and balanced characteristics is achievable by properly
deteriorating the axial aberration and off-axis aberration of the
lens. This is carried out by properly adjusting the satisfaction
levels of the conditions (1) to (3) when designing the lens.
[0264] To find a proper aspherical shape for a lens, an angle (an
incident angle) between a normal to the first surface of the lens
at the height of a highest ray and an optical axis must conform to
a conditional formula. Otherwise, the lens may not secure an
eccentricity tolerance and increase axial aberration or off-axis
aberration, thereby causing an aberration imbalance. This will be
explained in detail.
[0265] The present inventor designed many aplanats that
substantially perfectly satisfy the conditions (1) and (2) and meet
the condition (3) as high as possible with different focal lengths,
lens thicknesses, and glass materials of different refractive
indexes. From studies conducted on these lenses, the present
inventor found that the incident angle of a highest ray on the
first surface of a lens controls axial aberration, off-axis
aberration, and eccentricity aberration. A preferable design
wavelength for a lens is 450 nm or below, more precisely, 405
nm.
[0266] FIG. 22 shows the geometries of one of the lenses tested by
the present inventor.
[0267] A highest ray L0 is in parallel with an optical axis and
enters a first surface 10 of the objective 110. At an incident
point on the first surface 10, the ray L0 forms an incident angle
.theta. relative to a normal N. The lens 110 has a second surface
20.
[0268] FIGS. 23A and 23B are graphs showing relationships between
incident angle on the first surface 10 and aberration. FIG. 23A
shows off-axis aberration caused by an oblique ray of 0.5 degrees.
This off-axis aberration increases as an incident angle on the
first surface 10 increases. A black rhombus represents a lens made
of a glass material having a refractive index of 1.55, a white
rhombus a lens made of a glass material having a refractive index
of 1.65, a white triangle a lens made of a glass material having a
refractive index of 1.75, a white circle a lens made of a glass
material having a refractive index of 1.8, and a white square a
lens made of a glass material having a refractive index of
1.85.
[0269] FIG. 23B shows aberration caused by a surface-to-surface
eccentricity of 3 .mu.m. A black square indicates a lens made of a
glass material having a refractive index of 1.55, a cross a lens
made of a glass material having a refractive index of 1.65, a white
triangle a lens made of a glass material having a refractive index
of 1.75, a white square a lens made of a glass material having a
refractive index of 1.8, and a black rhombus a lens made of a glass
material having a refractive index of 1.85.
[0270] FIGS. 23A and 23B show that aberration increases are
substantially linear relative to incident angles on the first
surface, although they vary depending on lens design specifications
including lens focal lengths, lens thicknesses, and glass material
refractive indexes and design techniques including an aspherical
coefficient approximation. Axial aberration is properly corrected
in each case to 0.006.lambda. or below.
[0271] The relationships shown in FIGS. 23A and 23B are general.
Namely, the similar aberration characteristics appear for the same
incident angle irrespective of glass material refractive indexes,
lens thicknesses, or the radiuses of curvature of the vertexes of
the first surfaces.
[0272] To design a lens having a proper eccentricity tolerance and
off-axis aberration, a lens shape having an aberration of
0.04.lambda. or below with respect to an eccentricity of 3 .mu.m
and an off-axis aberration of 0.03.lambda. with respect to an
oblique incident light of 0.5 degrees is employed. In addition, the
conditions (1) to (3) are properly adjusted for the lens.
[0273] Adjusting the conditions (1) to (3) is equal to balancing
the conditions (1) to (3) by, for example, securing an eccentricity
tolerance while slightly sacrificing the axial or off-axis
aberration of the lens.
[0274] As mentioned above, a lens according to any one of the
embodiments of the present invention is an aplanat that
substantially satisfies the conditions (1) and (2) to substantially
zero the axial aberration and off-axis aberration of the lens and
slightly imperfectly satisfy the eccentricity aberration of the
lens.
[0275] When balancing the conditions (1) to (3) for a lens having a
numerical aperture of 0.85, a highest ray to the first surface of
the lens must have an incident angle of 57 degrees, preferably 56
degrees, more preferably 55 degrees or smaller. Balancing the
conditions (1) to (3) on a lens causes little change in the shape
of the lens.
[0276] To realize a lens having a numerical aperture of lower than
0.85 and substantially satisfying the conditions (1) to (3), it is
necessary to make a highest ray to the first surface of the lens
form an incident angle of 57 degrees, preferably 56 degrees, more
preferably 55 degrees or below.
[0277] When forming a lens according to an embodiment of the
present invention with the use of a metal mold, an incident angle
directly relates to the difficulty of processing the metal mold. It
is preferable to minimize the incident angle.
[0278] The shape of a metal mold prepared for a lens may slightly
differ from the shape of a product lens formed from the metal mold
because a high-temperature forming process on the metal mold
shrinks the lens. It is convenient, when manufacturing a lens
having a numerical aperture of lower than 0.85, to reduce an
incident angle accordingly.
[0279] The present inventor designed and studied many lenses and
found that an incident angle .theta. on the first surface of a lens
having a numerical aperture lower than 0.85 has the following
relationship with respect to an incident angle .alpha. of a lens
having a numerical aperture of 0.85:
.theta.=.alpha.-47.3(0.85-NA)(degrees) (9)
[0280] where the incident angle .alpha. is a value obtained from an
actually designed lens.
[0281] Table 14 shows a relationship between numerical aperture and
incident angle found on lenses made according to specifications of
the below-mentioned embodiment 4. The formula (9) is a regression
formula obtained from Table 14.
14 TABLE 14 Numerical aperture Incident angle (degrees) 0.60
39.8765 0.65 43.0969 0.70 46.2232 0.75 49.1485 0.80 51.6474 0.85
53.2516
[0282] FIG. 24 is a graph showing relationships between numerical
aperture and incident angle. .alpha. is 53.2516. In FIG. 24, a
black rhombus represents an actual design value, and a continuous
line represents values calculated from the regression formula.
[0283] FIG. 24 also shows data concerning lenses having a lens
thickness of 1.5 mm and a glass material refractive index of 1.75
with a black triangle representing design data and a dotted line
representing values calculated from the regression formula.
[0284] In each case, the regression formula satisfactorily reflects
the design values. The present inventor prepared design data for
many other lenses and obtained similar results. Consequently, it is
understood that the regression formula (9) has a sufficient
accuracy as a general formula.
[0285] Incident angle conditions for a lens having a numerical
aperture below 0.85 will be considered. As the numerical aperture
of a lens decreases, an inclination of the periphery of the lens
(an incident angle on the first surface of the lens) becomes
gentler, to relieve the conditions (1) to (3) and expand a
manufacturing tolerance.
[0286] Like the lens having a numerical aperture of 0.85, the lens
having a numerical aperture below 0.85 shows an aberration increase
as an incident angle on the first surface of the lens
increases.
[0287] Accordingly, the lens having a numerical aperture below 0.85
may properly be designed by setting an incident angle of 57
degrees, preferably 56 degrees, more preferably 55 degrees or
below, like the lens having a numerical aperture of 0.85. The lens
having a numerical aperture below 0.85 has the advantages mentioned
above. Accordingly, design values for the lens having a numerical
aperture below 0.85 may be moderated based on the regression
formula, to improve the tolerance and performance of the lens.
[0288] Namely, the lens having a numerical aperture below 0.85 may
properly be formed by setting an incident angle .theta. on the
first surface of the lens as follows:
.theta.<.alpha.-47.3(0.85-NA)(degrees) (10)
[0289] where the angle .alpha. is 57 degrees, preferably 56
degrees, more preferably 55 degrees.
[0290] The lenses mentioned above may have a proper eccentricity
tolerance but are unsatisfactory in securing chromatic aberration
because they give no consideration on the conditions (4) and (5).
The chromatic aberration will be explained in detail.
[0291] To satisfy the conditions (4) and (5), the thickness t along
optical axis through the center of a lens and focal length f of a
lens must satisfy the following condition:
t>(1+E)f
[0292] where E is a number equal to or large than 0, preferably 0,
more preferably 0.1, still more preferably 0.2.
[0293] According to the condition (4), an aberration increase at
the best focus of a lens must be minimized with respect to an error
in each wavelength. As the thickness along optical axis through the
center of a lens becomes thicker, the radius of the first surface
(incident surface) of the lens becomes relatively larger. Namely,
as the radius of curvature of the first surface becomes greater, a
ray entering the periphery of the lens makes a smaller incident
angle .theta. (an angle between a normal to the first surface and
the ray). This results in reducing a refraction effect, which is a
nonlinear phenomenon, and reducing spherical aberration with
respect to a wavelength error.
[0294] As explained with reference to FIG. 7, an aberration of
0.04.lambda. or greater occurs when the thickness of a lens becomes
thinner than the focal length of the lens. The aberration greatly
increases when the lens thickness becomes thinner than 3 mm, which
is 1.2 times the focal length. In addition, FIG. 8 shows that the
larger the lens thickness, the better the axial chromatic
aberration.
[0295] Consequently, a lens that satisfies the above-mentioned lens
thickness and highest-ray incident angle on the first surface may
simultaneously satisfy the conditions (1) to (3) in connection with
axial aberration, off-axis aberration, and eccentricity tolerance,
as well as the conditions (4) and (5) concerning wavefront
aberration and chromatic aberration caused by wavelength
errors.
[0296] An aspherical lens according to an embodiment of the present
invention may be a lens having a rotational symmetry shape around
an optical axis (coaxial optical system), or a toric lens having
slightly different aspherical shapes in different directions. An
incident angle of a highest ray on the toric lens must be within
the above-mentioned range.
[0297] Objectives for optical disks according to other embodiments
of the present invention will be explained.
[0298] In the following embodiments, an aspherical surface of a
lens is expressed with the following polynomial:
Z=CR.sup.2/(1+(1-(1+K)C.sup.2R.sup.2).sup.0.5)+AR.sup.4+BR.sup.6+CR.sup.8+-
DR.sup.10+ER.sup.12+FR.sup.14
[0299] where Z is a distance from the vertex of the surface, R is a
height from an optical axis, K is a conic constant, and A to F are
aspherical coefficients of degrees 4 to 14. For example, A is a
coefficient for R.sup.4.
[0300] Embodiment 4
[0301] FIG. 25 is a sectional view showing an objective according
to the embodiment 4 of the present invention. This lens is referred
to as the lens 11.sub.04.
[0302] A light flux L enters the lens 11.sub.04, is refracted by a
first surface 1 and a second surface 2 of the lens 11.sub.04, is
transmitted through a third surface 3 and transmission layer of an
optical disk 21, and is focused on a signal recording plane of the
optical disk 21.
[0303] Table 15 shows the specifications of the lens 11.sub.04.
15 TABLE 15 Design wavelength 405 nm Numerical aperture 0.85 Focal
length 2 mm Entrance pupil diameter 3.4 mm Disk thickness 0.1 mm
Image magnification 0
[0304] Table 16 shows design values for the lens 11.sub.04. Units
for radiuses and thicknesses are mm in Table 16 and in other tables
that follow.
16TABLE 16 Surface Surface Thick- Refractive Conic No. shape Radius
ness Index constant 1 Aspheric 1.71 2.75 1.85 -0.9168291 2 Aspheric
-75.9027 0.4605 -- 2518.06 3 -- Infinite 0.1 1.62230752 -- Image --
-- -- -- -- surface
[0305] Table 17 shows aspherical coefficients for the first surface
of the lens 11.sub.04.
17 TABLE 17 Coefficient for R.sup.4 0.013687371 Coefficient for
R.sup.6 0.00087533585 Coefficient for R.sup.8 0.00087533585
Coefficient for R.sup.10 -0.00077467164 Coefficient for R.sup.12
0.00030433925 Coefficient for R.sup.14 -5.3502493 .times.
10.sup.-5
[0306] Table 18 shows aspherical coefficients for the second
surface of the lens 11.sub.04.
18 TABLE 18 Coefficient for R.sup.4 0.22363727 Coefficient for
R.sup.6 -0.58889528 Coefficient for R.sup.8 0.72567392 Coefficient
for R.sup.10 -0.47382503 Coefficient for R.sup.12 0.12985027
[0307] The incident angle of a highest ray on the first surface of
the lens 11.sub.04 is 53.25 degrees. The lens 11.sub.04 is an
aplanat that substantially satisfies the conditions (1) and (2) and
leaves little error in the condition (3).
[0308] The lens 11.sub.04 involves an axial wavefront aberration of
0.002.lambda., which is very small and is substantially zero in
practical use. The lens shows a wavefront aberration of
0.023.lambda. for an incident ray of 0.5 degrees in off-axis angle.
This value is satisfactory. With respect to a surface-to-surface
eccentricity of 3 .mu.m, the lens shows a wavefront aberration of
0.036.lambda.. This aberration concerning the surface-to-surface
eccentricity is critical when manufacturing the lens, and the
aberration demonstrated by the lens 11.sub.04 is satisfactorily
small.
[0309] FIG. 26 is a graph showing a longitudinal aberration of the
lens 11.sub.04, FIG. 27 is a graph showing an offense against the
sine condition of the lens 11.sub.04, and FIG. 28 is a graph
showing an astigmatism of the lens 11.sub.04.
[0310] The thickness of the lens 11.sub.04 is 1.375 times the focal
length thereof. The lens 11.sub.04 is made of glass material having
a fixed refractive index. A wavelength change of 5 nm may change
the refractive index to 1.8486, to cause an aberration of
0.01.lambda. on a best image plane. This aberration is small. An
axial chromatic aberration is 2.17 .mu.m, which is also small.
[0311] Embodiment 5
[0312] FIG. 29 is a sectional view showing an objective according
to the embodiment 5 of the present invention. This lens is referred
to as the lens 11.sub.05.
[0313] A light flux L enters the lens 11.sub.05, is refracted by a
first surface 1 and a second surface 2 of the lens 11.sub.05, is
transmitted through a third surface 3 and transmission layer of an
optical disk 21, and is focused on a signal recording plane of the
optical disk 21.
[0314] Table 19 shows specifications of the lens 11.sub.05.
19 TABLE 19 Design wavelength 405 nm Numerical aperture 0.8 Focal
length 1.750 mm Entrance pupil diameter 2.8 mm Image magnification
0
[0315] Table 20 shows design values for the lens 11.sub.05.
20TABLE 20 Surface Surface Thick- Refractive Conic No. shape Radius
ness Index constant I Aspheric 1. 45 2.5 1.75 -0.9753354 2 Aspheric
-3.613636 0.395 -- -- 3 -- Infinite 0.1 1.62230752 -188.2991 Image
-- -- -- -- -- surface
[0316] Table 21 shows aspherical coefficients for the first surface
of the lens 11.sub.05.
21 TABLE 21 Coefficient for R.sup.4 0.023305393 Coefficient for
R.sup.6 0.017039056 Coefficient for R.sup.8 0.0023431785
Coefficient for R.sup.10 -0.0023798936 Coefficient for R.sup.12
0.0013373117 Coefficient for R.sup.14 -0.00035090993
[0317] Table 22 shows aspherical coefficients for the second
surface of the lens 11.sub.05.
22 TABLE 22 Coefficient for R.sup.4 0.17601287 Coefficient for
R.sup.6 -0.54949768 Coefficient for R.sup.8 0.50420582 Coefficient
for R.sup.10 0.12942116 Coefficient for R.sup.12 -0.37309714
[0318] The incident angle of a highest ray on the first surface of
the lens 11.sub.05 is 51.41 degrees. This angle satisfies the
condition (9) that specifies 52.63 degrees for a numerical aperture
of 0.8.
[0319] The lens 11.sub.05 is an aplanat that substantially
satisfies the conditions (1) and (2) and leaves little error in the
condition (3). The lens 11.sub.05 involves an axial wavefront
aberration of 0.001.lambda., which is very small and is
substantially zero in practical use.
[0320] The lens 11.sub.05 shows a wavefront aberration of
0.013.lambda. for an incident ray of 0.5 degrees in off-axis angle.
This value is satisfactory. With respect to a surface-to-surface
eccentricity of 3 .mu.m, the lens shows a wavefront aberration of
0.023.lambda.. This aberration concerning the surface-to-surface
eccentricity is critical when manufacturing the lens, and the
aberration demonstrated by the lens 11.sub.02 is satisfactorily
small.
[0321] FIG. 30 is a graph showing a longitudinal aberration of the
lens 11.sub.05, FIG. 31 is a graph showing an offense against the
sine condition of the lens 11.sub.05, and FIG. 32 is a graph
showing an astigmatism of the lens 11.sub.05.
[0322] The thickness of the lens 11.sub.05 is 1.429 times the focal
length thereof. The lens 11.sub.05 is made of glass material having
a fixed refractive index. A wavelength change of 5 nm may change
the refractive index to 1.7486, to cause an aberration of
0.01.lambda. on a best image plane. This aberration is small. An
axial chromatic aberration is 2.10 .mu.m, which is also small.
[0323] Embodiment 6
[0324] FIG. 33 is a sectional view showing an objective according
to the embodiment 6 of the present invention. This lens is referred
to as the lens 11.sub.06.
[0325] A light flux L enters the lens 11.sub.06, is refracted by a
first surface 1 and a second surface 2 of the lens 11.sub.06, is
transmitted through a third surface 3 and transmission layer of an
optical disk 21, and is focused on a signal recording plane of the
optical disk 21.
[0326] Table 23 shows specifications of the lens 11.sub.06.
23 TABLE 23 Design wavelength 405 nm Numerical aperture 0.85 Focal
length 2.2 mm Entrance pupil diameter 3.74 mm Disk thickness 0.1 mm
Image magnification 0
[0327] Table 24 shows design values for the lens 11.sub.06.
24TABLE 24 Surface Surface Thick- Glass Conic No. shape Radius ness
material constant 1 Aspheric 1.812171 3.104 NBF1 -0.3371789 2
Aspheric -6.507584 0.500289 -- -845.6516 3 -- Infinite 0.1 Polycar-
-- bonate 4 Image -- -- -- -- surface
[0328] Table 25 shows aspherical coefficients for the first surface
of the lens 11.sub.06.
25 TABLE 25 Coefficient for R.sup.4 -0.00092006967 Coefficient for
R.sup.6 -0.00025706693 Coefficient for R.sup.8 -0.00057872391
Coefficient for R.sup.10 0.0002222827 Coefficient for R.sup.12
-5.6787923 .times. 10.sup.-5
[0329] Table 26 shows aspherical coefficients for the second
surface of the lens 11.sub.06.
26 TABLE 26 Coefficient for R.sup.4 0.061448774 Coefficient for
R.sup.6 -0.13995629 Coefficient for R.sup.8 0.12867014 Coefficient
for R.sup.10 -0.043733069
[0330] Table 27 shows refractive indexes of the glass
materials.
27 TABLE 27 NBF1 1.76775590 Polycarbonate 1.62031432
[0331] The incident angle of a highest ray on the first surface of
the lens 11.sub.06 is 55.0 degrees.
[0332] The lens 11.sub.06 is approximately an aplanat that
substantially satisfies the condition (1), is slightly
unsatisfactory for the condition (2) so that the lens 11.sub.06 may
suppress eccentricity aberration more than the lens 11.sub.04, and
leaves little error in the condition (3).
[0333] The lens 11.sub.06 involves an axial wavefront aberration of
0.006.lambda., which is very small and is substantially zero in
practical use. The lens shows a wavefront aberration of
0.069.lambda. for an incident ray of 0.5 degrees in off-axis angle.
This value is satisfactory. With respect to a surface-to-surface
eccentricity of 5 .mu.m, the lens shows a wavefront aberration of
0.034.lambda.. This aberration concerning the surface-to-surface
eccentricity is critical when manufacturing the lens, and the
aberration demonstrated by the lens 11.sub.06 is satisfactorily
small.
[0334] FIG. 34 is a graph showing a longitudinal aberration of the
lens 11.sub.06, FIG. 35 is a graph showing an offense against the
sine condition of the lens 11.sub.06, and FIG. 36 is a graph
showing an astigmatism of the lens 11.sub.06.
[0335] The thickness of the lens 11.sub.06 is 1.411 times the focal
length thereof. A wavelength change of 5 nm to 410 nm may cause an
aberration of 0.029.lambda. on a best image plane. This aberration
is small. An axial chromatic aberration is 2.21 .mu.m, which is
also small.
[0336] Embodiment 7
[0337] FIG. 37 is a sectional view showing an objective according
to the embodiment 7 of the present invention. This lens is referred
to as the lens 11.sub.07.
[0338] A light flux L enters the lens 11.sub.07, is refracted by a
first surface 1 and a second surface 2 of the lens 11.sub.07, is
transmitted through a third surface 3 and transmission layer of an
optical disk 21, and is focused on a signal recording plane of the
optical disk 21.
[0339] Table 28 shows specifications of the lens 11.sub.07.
28 TABLE 28 Wavelength to use 0.405 .mu.m Numerical aperture 0.85
Focal length 0.88 mm Entrance pupil diameter 1.496 mm Disk
thickness 0.1 mm Image magnification 0
[0340] Table 29 shows design values for the lens 11.sub.07.
29TABLE 29 Surface No. Surface shape Radius Thickness Refractive
Index Conic constant 1 Aspheric 0.73 1.26 1.750 -0.9974081 2
Aspheric -1.791429 0.173565 1 -189.377 3 -- Infinite 0.1 1.62230752
-- Image -- -- -- -- -- surface
[0341] Table 30 shows aspherical coefficients for the first surface
of the lens 11.sub.07.
30 TABLE 30 Coefficient for R.sup.4 0.19868545 Coefficient for
R.sup.6 -0.0061548457 Coefficient for R.sup.8 0.80023321
Coefficient for R.sup.10 -2.8911336 Coefficient for R.sup.12
5.5467879 Coefficient for R.sup.14 -4.4427687
[0342] Table 31 shows aspherical coefficients for the second
surface of the lens 11.sub.07.
31 TABLE 31 Coefficient for R.sup.4 1.5351846 Coefficient for
R.sup.6 -14.829258 Coefficient for R.sup.8 33.428793 Coefficient
for R.sup.10 126.25085 Coefficient for R.sup.12 -558.31863
[0343] According to the lens specifications, a recommended value
for R1, or a value for A of the formula (7) is calculated as 0.734
mm. From this recommended value, the design value deviates by
0.5%.
[0344] The lens 11.sub.07 is an aplanat that substantially
satisfies the conditions (1) and (2) and leaves little error in the
condition (3).
[0345] The lens 11.sub.07 involves an axial wavefront aberration of
0.002.lambda., which is very small and is substantially zero in
practical use. The lens shows a wavefront aberration of
0.008.lambda. for an incident ray of 0.5 degrees in off-axis angle.
This value is satisfactory. With respect to a surface-to-surface
eccentricity of 3 .mu.m, the lens shows a wavefront aberration of
0.037.lambda.. This aberration concerning the surface-to-surface
eccentricity is critical when manufacturing the lens, and the
aberration demonstrated by the lens 11.sub.07 is satisfactorily
small.
[0346] A highest ray to the lens 11.sub.01 forms an angle u1' in
the lens, and this angle provides sin(u1')=0.45. A recommended
value for sin(u1') calculated from the lens specifications, i.e., K
of the formula (8) is 0.4367. From this recommended value, the
design value deviates by 3.0%.
[0347] FIG. 38 is a graph showing a longitudinal aberration of the
lens 11.sub.07, FIG. 39 is a graph showing an offense against the
sine condition of the lens 11.sub.07, and FIG. 40 is a graph
showing an astigmatism of the lens 11.sub.07.
[0348] A working distance of the lens 11.sub.07 is 0.1735 mm, which
is sufficiently larger than a preferable working distance of 0.125
mm for a disk of 25 mm radius.
[0349] Embodiment 8
[0350] FIG. 41 shows an optical pickup according to the embodiment
8 of the present invention. The optical pickup 30 includes a blue
laser diode (LD) 31 serving as a laser source, a beam splitter 32,
an objective 33, and a photodetector (PD) and current-voltage
converter (I-V) 34.
[0351] The blue LD 31 emits a blue laser beam of, for example,
about 405 nm in wavelength. The beam splitter 32 separates the beam
traveling from the blue LD 32 to an optical disk 35 from a beam
traveling from the optical disk 35 to the PD and I-V 34. The
objective 33 is any one of the lenses of the above embodiments. The
PD and I-V 34 converts incident light into a current and into a
voltage.
[0352] The optical pickup 30 is capable of writing signals
(information) to the optical disk 35. Namely, the blue LD 31 emits
a blue beam modulated by a write signal. The modulated blue beam is
passed through the beam splitter 32 and objective 33 and is focused
on the optical disk 35. On the optical disk 35, the information is
written to a recording plane according to the intensity of the blue
beam from the optical pickup 30. For example, the information is
recorded as pits or phase changes in lands or grooves on the
optical disk 35.
[0353] The optical pickup 30 is also capable of reading a signal
from the optical disk 35. Namely, the blue LD 31 emits a beam of
predetermined intensity. The beam is passed through the beam
splitter 32 and objective 33 and is focused on the recording plane
of the optical disk 35, which reflects the beam. The reflected beam
from the optical disk 35 is passed through the objective 33 and
beam splitter 32 and is received by the PD and I-V 34, which
converts the received beam into a voltage. In this way, a signal
recorded as a pit in a land or groove on the recording plane of the
optical disk 35 is provided as a voltage.
[0354] Embodiment 9
[0355] FIG. 42 is a block diagram showing an optical disk
writer-reader or an optical disk reader according to the embodiment
9 of the present invention.
[0356] The optical disk writer-reader includes a PRML (partial
response maximum likelihood) block 50, a controller block 60, a
write compensation block 70, and the optical pickup 30 of FIG. 41.
According to the embodiment 9, the optical disk writer-reader
employs a 1-7RLL (run length limit) signal modulation method.
[0357] The PRML block 50 includes an A/D converter 51, a digital
equalizer 52, a tap coefficient controller 53, a phase shifter 54,
a PLL 55, and a Viterbi decoder 56. The controller block 60
includes a 1-7RLL processing unit 61.
[0358] The PRML block 50 receives a signal from the optical pickup
30 through a preamplifier and carries out a PRML signal process on
the received signal. The controller block 60 receives a signal from
the Viterbi decoder 56 of the PRML block 50, and the 1-7RLL
processing unit 61 processes the received signal. The write
compensation block 70 receives a signal from the controller block
60, and according to the received signal, drives the blue LD 31 of
the optical pickup 30 through an LD driver.
[0359] In this way, the optical disk writer-reader receives a
signal read by the optical pickup 30 from the optical disk 35,
decodes the received signal, and provides the decoded signal. In
addition, the optical disk writer-reader receives an input signal,
encodes and modulates the received signal, and writes the modulated
signal to the optical disk 35 through the optical pickup 30. The
write block of the optical disk writer-reader may be omitted, to
provide an optical disk reader.
[0360] Although the embodiments have used concrete values to
explain the objectives for optical disks, these values are not
intended to limit the present invention. The present invention is
applicable to a variety of objectives for optical disks without
departing from the scope of the present invention. The beam
splitter mentioned above may be a polarized beam splitter.
[0361] Optical disks applicable to the present invention may have
transmission layers of 0.01 mm to 0.3 mm thick. The objectives
according to the present invention may be made of optical glass
such as NBF1 and may have refractive indexes of 1.5 to 2.0.
[0362] The objectives according to the present invention may be
formed through optional manufacturing methods, such as a direct
forming method to cut or grind a glass material, a glass forming
method, a sol-gel glass forming method, and a method to form a
resin aspherical layer on a glass or plastic spherical lens
material.
[0363] As explained above, the present invention is capable of
providing an objective for an optical disk, made of a single
double-sided aspherical lens having a numerical aperture equal to
or greater than 0.75 and capable of minimizing axial aberration,
off-axis aberration, surface-to-surface eccentricity aberration,
and chromatic aberration. Also provided are an optical pickup
employing the objective and an optical disk writer-reader and an
optical disk reader each employing the optical pickup.
[0364] The entire contents of Japanese Patent Applications
P2001-289992 (filed Sep. 21, 2001), P2001-290001 (filed Sep. 21,
2001), P2002-118318 (filed Apr. 19, 2002), P2002-118489 (filed Apr.
19, 2002), P2002-197990 (filed Jul. 5, 2002) and P2002-197996
(filed Jul. 5, 2002) are incorporated herein by reference.
[0365] Although the invention has been described above by reference
to certain embodiments of the invention, the invention is not
limited to the embodiments described above. Modifications and
variations of the embodiments described above will occur to those
skilled in the art, in light of the above teachings. The scope of
the invention is defined with reference to the following
claims.
* * * * *