JPH0239010A - Aspherical single lens - Google Patents

Abstract

PURPOSE:To contrive the reduction in weight and the miniaturization of an optical head by satisfying specified conditions on an aspherical surface. CONSTITUTION:Both of a first surface and a second surface are composed of the aspherical surfaces, the surfaces are the aspherical surfaces expressed when a distance from an arbitrary point on the aspherical surface up to the contact plane surface of an aspherical top is denoted as X, a distance from such a point up to an optical axis is denoted as H, the reference curvature radius of a nu-th surface is shown by Rnu, the conic constant of the nu-th surface is shown by Knu and the aspherical coefficient of the nu-th surface is shown as Anu i (i=3, 4...), and simultaneously, conditions (1), (2) and (3) are satisfied. Provided that F is the focus distance of an aspherical single lens, D is the thickness on the optical axis of the aspherical single lens and N is a refraction factor to the using wavelength of the aspherical single lens. Thus, the aspherical single lens can be obtained in which an abberation correction is satisfactorily executed both on the axis and outside the axis through a parallel plate having the thickness of approximately 0.04F-0.111F.

Description

Detailed Description of the Invention (Technical Field of the Invention) The present invention relates to a single lens having an aspherical surface, and particularly relates to a single lens having an aspherical surface.
This relates to a double-sided aspherical single lens with a diameter of about 0.42 to 0.50.

(Prior Art) In recent years, optical discs such as video discs and compact discs have been widely used as record carriers with large storage capacities.

Furthermore, optical cards, which have advantages such as large storage capacity and good portability, are also attracting attention as optical record carriers similar to optical disks.

In order to record information with high density on this type of record carrier and to accurately reproduce recorded information, an objective lens used in an information recording/reproducing apparatus is required to have a resolution of several μm. That is, 0.
An objective lens with a NA greater than 4 is required.

Furthermore, in the objective lens for the above-mentioned use, it is necessary to provide a sufficient distance between the surface of the carrier such as an optical disk or an optical card and the objective lens to prevent contact between the two to avoid damage to the record carrier or the objective lens.

Furthermore, in the above-mentioned information recording/reproducing apparatus, the mainstream method is to move the objective lens in the optical axis direction or in a direction orthogonal to the optical axis direction in order to perform autofocus or autotracking. Therefore, in order to improve response characteristics, this type of objective lens is required to be smaller and lighter in weight.

Conventionally, as this type of objective lens, Japanese Patent Application Laid-Open No. 58-420
JP-A-21, JP-A-58-208719, JP-A-60122-915, etc. disclose lens systems having a configuration of four elements in four groups.

However, the objective lenses disclosed in these publications have a large overall length of the lens system, and cannot be made smaller and lighter as described above.

In order to eliminate the above-mentioned drawbacks, the development of aspherical single lenses has recently been active.
The technology is disclosed in Japanese Patent Publication No. 7, Japanese Patent Application Laid-open No. 11715/1983, and the like.

However, the aspherical single lens shown in the above publication was designed in accordance with the specifications of the optical disk, and the protective layer covering the information recording surface of an optical card or the like is thinner than that of the optical disk. It is extremely inappropriate when used against

The thickness of the optical card is about 0.8 mm, which is about the same as the thickness of commonly distributed magnetic cards, so when considering the strength of the optical card, the thickness of the transparent protective layer in the optical card t
is approximately 0.4 mm.

In the example of the aspheric single lens shown in the above-mentioned publication, if the focal length of the lens is F, then the thickness t of the transparent protective layer of the record carrier to which the lens shown in the example can be applied is
is about 0.26F to 0.28F. Therefore, the appropriate focal length F of the objective lens for the thickness t = 0.4 mm of the transparent protective layer in the optical card is 1.43 to 1.54.
It becomes mm.

However, in this case, there are disadvantages such as the radius of curvature is too small, making it extremely difficult to manufacture, and the area (image height) with good imaging characteristics that can be considered as diffraction limited is extremely small, making it almost impractical. Not the point.

Therefore, a practical countermeasure is to use a parallel plate interposed between the objective lens and the optical card for correcting the thickness of the protective layer. That is, the focal length of the objective lens of the conventional example is set to approximately F=4.5 mm, which is easy to manufacture. The thickness of the protective layer required at this time is 1.17 to 1.26 m.
On the other hand, since the thickness of the protective layer of the optical card is 0.4 mm, it is sufficient to use a parallel plate having a thickness of about 0.77 to 0.86 mm, which is the difference between them.

However, this method is also undesirable because it goes against the demands for improved performance by reducing the size and weight of the optical system and for cost reduction due to a reduction in the number of parts.

Furthermore, in an optical head used in an optical memory device that records information, the lens shown in the conventional example above can be used as a collimator lens that efficiently converts the divergent light beam from a semiconductor laser into a parallel light beam with little loss of light quantity. A similar drawback has been pointed out when using the laser.
This is because it is approximately 0.25 to 0.35 mm.

(Summary of the Invention) An object of the present invention is to eliminate the above-mentioned conventional drawbacks, and to reduce the thickness t from approximately 0.04F to 0.04F. 1° through the parallel plate of IIIF
It is an object of the present invention to provide an aspherical single lens in which aberrations are well corrected within a certain angle of view.

The above objects of the present invention are achieved by the aspheric single lens of the present invention described below.

(Example) The aspherical single lens according to the present invention is an aspherical single lens in which both the first and second surfaces are aspherical, and the aspherical surface is connected to the aspherical vertex from any point on the aspherical surface. The distance to the tangent plane is
When the aspherical coefficient of the surface is A, + (+=3.4...), it is an aspherical surface expressed by the following formula, and the following conditions (1), (2), and (3) are satisfied. A satisfying aspheric single lens.

and for properly correcting coma aberration.

According to "Lens Design Method" by Yoshiya Matsui (Kyoritsu Shuppan), the third-order spherical aberration coefficient of the first and second surfaces is 1. , I2 and the coma aberration coefficients TI, , II2 of the first surface and the second surface are expressed as follows when the entrance pupil coincides with the first surface and the object distance is infinite.

+ A 114H'+... (ν=1.2) However, F is the focal length of the aspherical single lens, D is the thickness of the aspherical single lens on the optical axis, and N is the wavelength of the aspherical single lens used. It is the refractive index.

Next, conditions (1) to (3) will be explained.

Conditions (1) and (2) of the present invention are spherical aberration II in the third-order region, = 2R1, where ψ1. ψ2 is a third-order aspherical term of the first surface and the second surface, respectively, RI is the paraxial radius of curvature of the first surface, and R2 is the paraxial radius of curvature of the second surface.

The third-order spherical aberration coefficient I and coma aberration coefficient II of the entire lens are the sum of the respective aberration coefficients of each surface, I=1.
+12 TI = II, + II 2 is determined, and the lens shape and each aspherical amount are determined so that I and II have appropriate values.

As is clear from the above equation, once the shape of the lens (focal length, working distance, etc.) is determined, R, , R2, and D.

The value of N is almost fixed, and the degree of freedom left to set the aberration coefficients I and ■ to appropriate values is ψ1. There is only ψ2.

Therefore, the lens shape must be determined with some consideration for aberration correction, and the numerical range for this is the condition (
1), (2).

If the numerical value range of condition (1) is exceeded, the spherical aberration of the first surface in particular becomes large, and the aberration cannot be corrected completely by the aspherical term φ1 of the first surface.

Condition (2) is a condition for comatic aberration to be well-balanced (corrected) on the second surface. If this value is outside this numerical range, the aspherical term ψ2 of the second surface will not be able to fully correct the aberration, and off-axis coupling will occur. Image performance deteriorates significantly.

Condition (3) is mainly a condition for satisfying the sine condition. In the present invention, not only on-axis aberration but also off-axis aberration within a certain range, especially coma aberration, is corrected well.
Outside the range of 3), isoplanatic conditions are significantly lost, which is undesirable. If the upper limit of the condition is exceeded, the radius of curvature of the first surface becomes too small (too much), negative spherical aberration will occur, making it difficult to correct the aberration, and the working distances W and D will become short, making it impractical. It has the disadvantage of causing the above disadvantages.

Examples of the aspheric single lens of the present invention are shown below.

However, as shown in Figure 1, F is the focal length of the lens, and NA
is the numerical aperture, β is the paraxial lateral magnification, R1 is the paraxial radius of curvature of the aspherical surface of the first surface, R2 is the paraxial radius of curvature of the aspherical surface of the second surface, D
is the center thickness of the lens, W, D are the working distance, t is the thickness of the parallel plate, N is the refractive index of the lens at the wavelength used λ = 830 nm, Nt is the refractive index of the parallel plate at the used wavelength λ = 830 nm, △v (j) (ν=1.2) is the optical axis direction of an aspheric surface in 10% of the lens effective diameter determined by NA (numerical aperture) and a spherical surface with paraxial radius of curvature R on the νth surface. difference (where △ and (j) are positive in the direction in which the curvature of the aspherical surface becomes weaker).

The shape of the aspherical surface is expressed as follows: X is the distance from any point on the aspherical surface to the tangent plane of the apex of the aspherical surface, H is the distance from the arbitrary point to the optical axis, R is the reference radius of curvature of the νth surface, , the conic constant of the νth surface is, , the aspherical coefficient of the νth surface is A□(i=3.
4. ), it is an aspherical surface expressed by the following formula.

+A, 4H'+... (ν=1.2) Moreover, FIG. 2, FIG. 3, FIG. 4, FIG. 5, and FIG. 6 respectively show Example 1 of the present invention. 2.3.4. FIG. 6 is an aberration diagram of lens No. 6. Here, spherical aberration, astigmatism K, =
6.28361 x 10-2A I3 = -2,
16317X 10-2A, 4=-4,24898
X10-2A, 5=-5,03660X 10-'A
, 6 = -1,36336X10゜A1□ = 1,54304X10゜A, 8 = 3.63946X10' A,, = 4.33953X10゜Aoo = -1,63823X10゜A+++ = -3,89130xlO゜A++2=
7.83997X10-' and distortion are shown,
SA represents spherical aberration, sc represents the amount of unsatisfactory sine condition, M represents curvature of field on the meridional surface, and S represents curvature of field on the sagittal surface.

Example work F=1. O R, = 0.68755 R2 = -2,27906 NA = 0.42 β = O D = 0.66529 N = 1.57532W -
D=0.58786 t=o, 08871 Nt=1.510K 2=
-7,00091x 10'A23= -3,35
328xlO-"A24= -3,37362XIO A2. = 1.75490X10 A2.= 3.64952xlO A27= -3,01,265X 10°A22.
= 2.47448XIO'A ,, = -2,8
5179x 10A210: 1.59293X1
0'A211: 4.51401X10-'A212
: -8,89595xlO-'AI+3"= Al14=Aos"=Al16": 3.70513X10-' 2.22663 00724 △, (9) = 0.00541 △, (7) = 0.00208 △+ (5) = 0.00051 A213 = 2.90965X lo -'A214=
5.13745X10-'A215=6.74
467 X 10-'A216= -1,11644X
10th Example 2 F=1. O R+ =0.68647 R2=-2,16986 A2 (to) A2(9) A2(7) A2(5) NA=0.42 D=0.73183 WD=0.55190 t=0.08871 = 0.00078 0.00086 0.00051 =O,0OO17 β=ON N=1.57532 Nt=1.510 K, = 5.20593X10-”A, 3=-
2,22406X 10-2A,, = -6,84
116X10→A+s= 3.08303X10-'
A, 6=-1,35893xlO6 A1□=7.34739 x 10A, 8=3
．． 24484xlO6 A,, = 4.54175xlO6Auo = 5
．． 93378xlO8 Am= -3,66118xlO-' Al12= 7.82079X10-'Al13=
3.34636X10-'AI+4=-2,201
91X 10-'Au5= 4.72685XIO-
'Aos= 1,55052x 10-'K 2=
−6,79105xlO A23= −1,13810×10−2A2. =-3
, 13410×10-A 2. = 7.17002 x 10-”A28
= 4.28976X10 A 2. =-2,50630X 10°A28=
4.67335xlO' A29 = -6,59390X 10°A210=
1.46333X10 Azo= 4,77442xlO-'A212: -
4,88410X 10-'A213= 2.443
66XIO-'A214: -2,42219X 10
-'A215= 5.84567X 10-'A21
6: -8,87000X 10-'△I (10)=
0.00657 △+ (9) = 0.00512 △, (7) = 0.00202 A1 (5) = O, 0O051 A2 (10) = 0.00152 A2 (9) = O, 0O112 A2 (7) = O,0O051 A2(5) =O,0OO15 Example 3 F = 1.0 R, = 0.68780 R2 = -2,10947 K, = 5.07475XIO-"A,, =
-2,33838X 10-2A,, = -4,
89668x 10” Al5= 3.76532x
tO-'A, 6=-1,23402XlO'A, 7=7.50548X10"A, 8=3.27949X10°A,,,=4.35688X10'Aoo=5
．． 89298XlO' Am=-3,73027x 10-'NA=0.42
β=OD=0.75403 N=1.57532W −
D=0.54087 t=0.08871 Nt=1.510K 2=
-7,00444X 10 A23= -1,55837x 10-"A24=
−3,30849xlO=A2. = 8.20143X, 0-”A 2I!=
4,98421 x 10”A 27= -2,4
9824X 10°A, = 3.57727X10
'A29=-6,88698XIO'A2+o=5.93651X10'A211:
5.21078X10-'AI+2=8.0803
7XlO-'A++3=3.40408X10-'
Al14=-2,18674X 10~6Aos=
4.58225XIO-'Aos=1.5405
2XlO-'△, (10)=0.00630 △, (9)=0.00496 △, (7)=0.00198 △+ (5)=O,0O050 A2I2= -2,49735X 10-'A213=
2.451.36X10zu A2+4: -2,99
231X 10-'A21s= 6.65433Xl
O-'A2111: -8,98316xlO-'△2
(lO) A2(9) A2(7) A2(5) =O,0O172 =0.00122 =O,0O053 =O,0OO16 Example 4 F =1. O R, = 0.68781 R2 = -2,02646 NA = 0.42 D = 0.79838 W −D = 0.51732 t = 0.08871 β = O N = 1.57532 Nt = 1.510 K, = 3.97960xlO-2A 5. =
-2,73614X 10-'A, 4=-2,06
205x 10-”A 15=-3,52632x
10-'A,, =-1,24433xlO0A, 7
= 7.21406X10A, 8=1.87860X10゜A 1g = 5.94830X10'Ano
= 6.10239X]O' Am= -3,353801x: 10-'Al12=
8.10202X10-'Al13=3.41
865X10-'A114=-2,18053X10
-'A month s= 4.01024X10-'Al16
:-1.67946XIO-'K2=-7,803
49XIO A23=-2,46279X 10-"A24=-
3,63186X10-'A2. = 6.5612
1 x 40”A, = 6.74671 x 10A
2. = -2,28982X 10°A28= 3
．． 619o6xlO6 A? , = -6,75624X 10'A210
: 1.17621 x 10”A2o=5
．． 21078X10-'A2+2=-2,49735
x 10-'A213: 2.48567X 10-
'A214=-2,43292X 10-'A215
: -3,73073X 10-'A216= -1,
02985X 10-'△+ (10)= 0.006
41 △+ (9) = 0.00492 A1 (7) = O, 0OI92 △, (5) = 0.00049 A2 (10) = O, 0O197 A2 (9) = O, 0O136 A2 (7) = 0. 00057 A2(5) =0.0OO17 Example 5 F =1. Q R, = 0.68756 R2 = -1,94683 K, = 3.05536xlO-'A, 3 =
-3,26784X 10-”A,, = 5.799
08xlO-"A, 5=-3,36915X10A, 6=-1,23850XIO'A, 7=6.45142xlOA,, = 1.88819X10°Al9=5.65378xlO'A11o=6.85574X10°A...= -3,
26935x 10'□6NA=0.42
β=O D=0.84270 N=1.57532'W
-D=0.49363 t=o, 08871 Nt=1.510K 2=
-7,56830X70 A 23= -3,47628X to -2A2.
= -3,21018X10-'A25= 1.20
435X10-'A26= 1,49034X10'A27=-3,59431X10' A28= 4.37917X10°A2. = 6.35230XIO6 A210= 8.77797X 10゜A21 +=
4.96850 x 10-'AI+2=8.
10270X 10-'Aoa= 3.48110x
lO-'Ao4=-2,18487X 10-'An
s= 3.59681 X 10-'A+6=-1
．． 92897X10-'A212=-2,33107
X10-'A213: 1.32798XlO-'
A214: -1,32597XlO-'A2+s=
-2,62954X10-'A2+6: 1.847
36X10-' has good imaging performance. That is, 0.06
5F<t<0. Good imaging performance can be obtained within the range of IIIF.

Example 1.2 described above. 3.4. In addition to the above-mentioned conditions (1) to (3), it is preferable for the lens shown in No. 5 to satisfy the following conditions (4) to (6).

△+(10)=0.00608 △2(10)=
0.00212△1(9)=0.00472△
2 (9) = 0.00147△, (7) = 0.001
87 △2(7) =O,0O059△+ (
5)”0.00049 △2(5) =0.0
0016 Example 1 shown above. 2. 3. 4. 5
In this case, the focal length F is 4.5 mm and the NA is 0.4.
2. It is designed so that the thickness t of the parallel plate is 0.4 mm, and has imaging performance close to the diffraction limit within a field angle range of approximately 10°. Furthermore, the thickness t of the parallel plate is equal to the above N
A.

Conditions (4) and (5) are good for correcting spherical aberration and coma aberration in the third-order region under the angle of view condition, which is good up to a variation of about ±0.1 mm.

If the numerical value range of condition (4) is exceeded, the spherical aberration of the first surface becomes particularly thick (and the aberration cannot be corrected completely by the aspherical term ψ1 of the first surface).

Condition (5) is a condition for correcting comatic aberration in a well-balanced manner on the second surface. If this value is outside this numerical range, the aspherical term ψ2 of the second surface will not be able to fully correct the aberration, resulting in off-axis imaging. Performance deteriorates significantly.

Condition (6) is mainly a condition for satisfying the sine condition. In the present invention, not only on-axis aberration but also off-axis aberration within a certain range, especially coma aberration, is corrected well.
If it is outside the range of 6), the isoplanatic condition will be significantly lost, which is undesirable.

If the upper limit of the condition is exceeded, the radius of curvature of the first surface will become too small, and a large amount of negative spherical aberration will occur, making it difficult to correct the aberration, and the working distances W and D will be short (which makes it difficult to use in practice). The disadvantage is that it causes the following problems.

In a single lens, by satisfying the following conditions (7) to (10) in addition to the conditions (1) to (6) described above, spherical aberration can be particularly well corrected.

(7) 0.005F <△, (10) <O,oo
8F (8) 0,0O18F <△, (7) <
0.0022F(9) 0.0005F < △2
(10)<0.0025F (10)0.0004F<
Δ2 (7) <0.0O07F Conditions (7) to (10) are conditions for determining the aspheric amount at 100% and 70% of the effective diameter of the first and second surfaces of the lens. Condition (7)
By satisfying the condition from (lO), spherical aberration in particular can be corrected even better.

If the upper limits of conditions (7) and (8) are exceeded, the spherical aberration becomes excessive, and conversely, if it falls below the lower limits, the spherical aberration becomes under, and the axial performance deteriorates.

Conditions (9) and (10) mainly relate to correction of off-axis aberrations, and when the range is outside the upper and lower limits, the amount of coma aberration increases and off-axis performance deteriorates.

For different corrections of spherical aberration, (11) 0.004F <△, (9) <
0.006F(12) O,0O04F <△, (5
) < O, 0o06F, and for different corrections of coma aberration, (13) O, 0O05F < A
2 (9) <, 0.002F (14) O, 0
It is preferable to satisfy the condition OOIF < A2 (5) < O, 0O02F in addition to the conditions (1) to (lO) described above.

Here, conditions (11) to (14) are conditions for determining the amount of asphericity at 90% and 50% of the effective system of the first and second surfaces of the lens.

Alternatively, in addition to the conditions (1) to (10) described above, it is preferable for aberration correction to satisfy the following condition (15).

Below the lower limit of condition (15), astigmatism worsens, while above the upper limit, comatic aberration remains, which is undesirable.

Other examples of the aspherical single lens of the present invention will be shown below.

However, as shown in Figure 1, F is the focal length of the lens, and NA
is the numerical aperture, β is the paraxial lateral magnification, R1 is the paraxial radius of curvature of the aspherical surface of the first surface, R2 is the paraxial radius of curvature of the aspherical surface of the second surface, D
is the center thickness of the lens, W, D are the working distance, t is the thickness of the parallel plate, N is the refractive index of the lens at the wavelength used λ = 830 nm, Nt is the refractive index of the parallel plate at the used wavelength λ = 830 nm, △v (D (ν=1.2) is NA on the second surface
The difference (
However, △ and (j) are positive in the direction in which the curvature of the aspherical surface becomes weaker. ).

The shape of the aspherical surface is defined by the distance from an arbitrary point on the aspherical surface to the tangent plane of the aspherical apex, and the distance from the arbitrary point to the optical axis to H1, the standard radius of curvature of the νth surface. R,, the conic constant of the second surface is, , the aspherical coefficient of the second surface is A, i (
i=3. 4. ), it is an aspherical surface expressed by the following formula.

Also, Figure 7.

Figure 8.

+A, 4H'+... (ν=1.2) FIGS. 9, 10, and 1I show examples 6.7.8.9. of the present invention, respectively. 10 is an aberration diagram of lens No. 10. Here, spherical aberration, astigmatism, and distortion are shown, where SA is the spherical aberration, SC is the amount of unsatisfactory sine condition, M is the curvature of field of the meridional surface, and S is the curvature of field of the sagittal surface.

Example 6 F = 1. O R,=0.68754 R2 knee 2.07077 NA=0.47 β=O D=0.77662 N=1.57532W・
D=0.54341 t=0.06653 Nt=1.510K 2=
-7,00400X 10'A 23= -1,7
2085X 10-”A2. = -2,35772X
10 A25=-3,52770xtO- A26=1.62899xlO6 A2. = -4,02051X 10°A28=2
゜13750X10-'A29=1.45131x10'A210
= 6.48502X 10°A2+1= 4.7
6052XIO-'K, = 2.22488X1
0-”A, 3=-2,14320X10-”A,
, = -5,19200X10-2A ,, = -2
,96041x 10-'A +e =-1,2654
4X10'A, = 8.42816xlO-'A, 8=2.04761 x 10°A,,
= 5.32620 x 10゜ + o = 5.1
4725XIO' A+++= -3,33063X 10-'AI+2=
7.88360X10-'Ao3=2.863
41X10-'Al14=-1,82936X 10
-'Aos= 3.44032X10-'AI+6=
-1,90544X10-'A212: -], 35
632X10-'A2+3= 1.07469X10
-'Az+4=-1.65195X 10-'A215
: 5.95045X10-'A2+6=-1,4
3275 ) A2(5) Example 7 F = 1. O R, = 0.68814 R2 = -1,97884 NA = 0.47 D = 0.82172 WD = 0.51983 t = 0.06654 = 0.00289 = 0.00211 = 0.00098 = 0. 00031 β=O N=1.57532 Nt=1.510 K, = 3.43328xlO-'A, 3=
−2,49918xlO−”A,, = −4,54
385x to −”A,, = −2,83119X
10 ”'A l6=-1,24364X10°A, 7= 7.83725X10-'A l8=
1.84642X10°A,,=5.43972
X 10OAno= 4.94049X100 A+n = -3,33180X 10-'Al12=
8.01624X to -'Al13: 3.
40693X to −'An4= −2,05618
X 10-'Aos= 3.43040X10-'A
os=-1,13037X 10-'K 2=-7
,21457X10' A 23= -2,64123X to -”A2.=
-3,18729X10- A25= -1,26877xlO-'A, = 2
．． 20196X10' A 27= -4,87064X 10°A , = -
1,00041X 10-'A2. = 1.435
13X10'A+o=4.19918X10-'A
211= 3.28153X10-'A212: -
1,35856X10-'A213= 1.1673
6Xlo-'A214=-1,66002Xlo-'
A215= 5.10681 X 10-'A216
= -1,55776X10-'△, (10) = 0.0
0647 △, (9) = 0.00657 △+ (7) = 0.00299 △, (5) = 0.00077 △2 (10) △2 (9) △2 (7) △2 (5) = 0 .00304 =0.00218 =0.0O095 =0.00028 Example 8 F =1.0 R, =Q, 68746 R2 knee 1.90418 K, = 3.43135X10-2A, 3=
−2,81689xlO−”A,, = −3,30
653X 10-2A,, = -2,56224x
10A, 6=-1,23347X10'A,? = 7,64429XIOA,, =
1.60759X10°A,, = 5.49206
XIO1lAoo= 5.18999X10゜Am=-3,29995X 10-'NA=0.47
β=OD=0.86611 N=1.57532W-
D=0.49581 t=0.06654 Nt=1.510K 2=
-7,45115xlO A 23= -3,58902x 10-”A ,,
= -3,22769X 10''A, = 1.
10918xlO- A28 = 1.99634XIO' A, = -4,40615XIO' A, = 3.20784XIO"" A2. = 1.43888X10'A210= -
2,50794X10 A211= 3.69678X10-'Al12=
8.04748X10-'A port 3=3.396
78xlO-'Ao4=-2,02564xlO-5
Aos= 3.38730XIO-'Al16=-
6,12022X 10-'△I (10)=0.00
594 △+ (9)=0.00622 △I (7)=0.00288 △+ (5)=0.0O075 A212= -4,3628X10-'A213:
6.14399X10-”A214=-4,0326
8X10-'A215= 1.16566XIO-'
A216=-1,10195XIo-'Example 9 F=1.0 R,=0.68867 R2=-1,84771 △2 (to) 2(9) △2(7) △2(5) NA= 0.47 D=0.88889 W-D=0.48446 t=0.06667 =0.00334 =0.00238 =0.00101 =0.00029 β=O N=1.57532 Nt=1.510 K , = 3.17260X10~2A , 3=
-2,32442x 10-2AI4”5゜41829
XIO-" A,, = -2,82427X 10A, 6=-
1,04034XlO6 A1□= 7.97214X10-'A, 8= 1
．． 75503X10' A,, = 5.32803 x 10゜Aoo=
-1,31536X 10'Au+= -3,32
477X 10-'Al12= 1.02202X1
0-'A++3= 2.86361 X 10-'A
I+4: -1,84403X 10-'A++s=
3.31557X10-'Ana=-2,6534
9X 10-"K 2 = -6,78021X 10 A, = -3,80066X 10-"A 2. =
-2,50428X October A25= -7,033
30xlO-”A, = 1.87137xlo' A, =-2,68110X 10°A 28=-
2,85849X to.

A29= 9.92178XIO' A210= -1,49024X10 A2o= -2,20336xlO-5Az+2==
-7,27432x 10-'A2+3= 1.16
742X 10-'A214: -3,l1163X1
0-'A215=-2,34088X 10-'A2
16=-1,08451X 10"6, (10)=0
．． 00816 1(9)=0.00686 , (7)=0.00289 + (5)=0.00074 A2 (10) A2(9) A2(7) A2(5) =0.00332 =0.00236 = 0.00099 =O,,0O028 Example 10 F = 1.0 R, = 0.68673 R2 = -1,78956 NA = 0.47 β = OD = 0.931
47 W-D=0.46057 t=o, 06653 Nt=1.510K 2
= -7,11075xlO' A 23= -4,51875x 10-"A2. =
-2,28284X10'A,l=-6,010
62X10-”A26= 1.92250xlO6 A2.=-8,92777X10”A28=
1. o0164XlO-'A 29= 6.91
414 X 10-'A210= -8,43895X
10'A211=-3,08490X 10-'
N=1.57532 AlI3: 1.43247X 10-5AI+3:
2.84211X10-'An4=-2,774
70X 10-'Aos= 3.33257X10-
'AIIa==4.88828X 10-'A21
2= 4.39181 X 10-'A2+3=
9.03455X 10-'A214: 9.383
76X10-'A215= 4.99674X10-
'A2+6==-1,61383X10-'K,
= 3.06362X10-'A, 3=-2,6
0717X 10-”A, 4=-3,09516x
10-”A, 5=-2,79953XIO”A
, 6=-1,19755XIO'A, 7=7,98588XIO-'A, 8=
2.91033X10'A,,=5.21606
XIO6Auo=-8,51268x 10'A+n
= -3,31804X 10-'Δ1(10)=0.
01014 A2(10)=0.00343△+
(9) = 0.00739 to 2 (9) = 0.
00244△, (7)=0.00289 A2(
7) =0.0O101△, (5) =0.0O073
Example 6 where A2(5) = 0.00028 or more.
7.8.9. 10, the focal length F is 4 or 5
mm, NA is 0.47, and the thickness t of the parallel plate is 0.
It is designed to have a diameter of 3 mm, and has imaging performance close to the diffraction limit within an angle of view of approximately 10°. Furthermore, the thickness t of the parallel plate is the above NA.

Under the conditions of the angle of view, it has good imaging performance up to a variation of about ±0.1 mm. That is, 0.04F < t < 0
．． Good imaging performance can be obtained within the range of 09F.

As seen in Examples 6, 7.8.9.10 above, in addition to the conditions (1) to (3) above, the following conditions (16) to (18) must be satisfied. is preferred.

Condition (I7) is a condition for well-balanced (correcting) comatic aberration on the second surface. If this numerical value range is exceeded, the aspherical term ψ2 of the second surface cannot fully correct the aberration (and the off-axis Imaging performance deteriorates significantly.

Condition (18) is mainly a condition for satisfying the sine condition. In the present invention, off-axis aberrations within a certain range, especially comatic aberration, are well corrected as well as on-axis aberrations, but outside the range of condition (18), the isoplanatic condition is significantly lost, which is undesirable. It is something. If the upper limit of the condition is exceeded, the radius of curvature of the first surface will become too small, and a large amount of negative spherical aberration will occur, making it difficult to correct the aberration, and the working distances W and D will be short (which makes it difficult to use in practice). Conditions (16) and (17), which have the drawback of causing the following disadvantages, are intended to satisfactorily correct spherical aberration and coma aberration in the third-order region.

When the numerical value range of condition (16) is exceeded, the spherical aberration of the first surface in particular becomes large, and the aberration cannot be corrected completely by the aspherical term ψ of the first surface.

For lenses, the above-mentioned (1) to (3) and (16)
In addition to the conditions (19) to (18), the following conditions (I9) to (22) can be satisfied to particularly favorably correct spherical aberration.

(19) 0.005F<△, (10)<O,01
IF(20) 0.0027F<・△, (7)
<0.0032F(21) 0.0027F<△2
(lo)<o,ooa6F(22) 0.0O09F
<Δ2 (7) <0.0011F Conditions (19) to (22) are conditions for determining the aspheric amount at 100% and 70% of the effective diameter of the first and second surfaces of the lens. Condition (19
) to (22), spherical aberration in particular can be corrected even better.

If the upper limits of conditions (19) and (22) are exceeded, the spherical aberration becomes excessive, and conversely, if it falls below the lower limits, the spherical aberration becomes under, and the axial performance deteriorates.

Conditions (19) and (22) mainly relate to correction of off-axis aberrations, and when the range is outside the upper and lower limits, the amount of coma aberration increases and off-axis performance deteriorates.

For different corrections of spherical aberration, (23) 0.006F <△+ (9) < 0
．． 008F(24) O,0O07F <△, (5)
< 0.0008F, and for different corrections of coma aberration (25) 0.002F <
△2 (9) < 0.003F (26) O,
The conditions 0O02F <△2(5) < 0.0003F are determined from (1) to (3) and (16) to (
It is preferable that condition 18) is also satisfied.

Here, conditions (23) to (26) are conditions for determining the aspheric amount at 90% and 50% of the effective system of the first and second surfaces of the lens.

Alternatively, in addition to the conditions (1) to (3) and (16) to (18) described above, it is preferable for aberration correction to satisfy the following condition (27).

Below the lower limit of condition (27), astigmatism worsens, while above the upper limit, comatic aberration remains, which is undesirable.

Other examples of the aspherical single lens of the present invention will be shown below.

However, as shown in Figure 1, F is the focal length of the lens, and NA
is the numerical aperture, β is the paraxial lateral magnification, R2 is the paraxial radius of curvature of the aspherical surface of the first surface, R2 is the paraxial radius of curvature of the aspherical surface of the second surface, D
is the center thickness of the lens, W and D are the working distance, t is the thickness of the parallel plate, N is the refractive index of the lens at the wavelength used λ = 830 nm, and Nt is the refraction of the parallel plate at the used wavelength λ = 830 nm. The ratio, Δp (D (ν=1.2), is the optical axis direction of the aspheric surface in 10% of the lens effective diameter determined by NA (numerical aperture) on the νth surface and the spherical surface with paraxial radius of curvature R1. difference (where △ and (j) are positive in the direction in which the curvature of the aspherical surface becomes weaker).

The shape of the aspherical surface is expressed as follows: X is the distance from any point on the aspherical surface to the tangent plane of the apex of the aspherical surface, H1 is the distance from the arbitrary point to the optical axis, R3 is the standard radius of curvature of the νth surface, Let the conic constant of the νth surface be , and the aspherical coefficient of the νth surface be A v+ (+
=3. 4. ), it is an aspherical surface expressed by the following formula.

+ A v 4H'+... (S2 1, 2) In addition, FIGS. 12, 13, and 14 show Example 11 of the present invention, respectively. 12. 13 is an aberration diagram of lens No. 13.

Here, spherical aberration, astigmatism, and distortion are shown, where SA is the spherical aberration, SC is the amount of unsatisfactory sine condition, M is the curvature of field of the meridional surface, and S is the curvature of field of the sagittal surface.

Example 11 F = 1.0 R, = 0.68769 R2 = -2,38714 NA = 0.50 β = O D = 060633 W fist = 0.61924 t = 0.08871 Nt = 1.510K
2= -6,Q9045XIO A 23= -7,19034x 10-2A 24=
-2,01016x 10-”A, = -5,04
343X 10-'A, = 1.33064X10°A, = -3,78361X100 A, = 4.48779xlO6 A 2. = -2,95692X 10°A210=
-1,38834X1O N=1,57532K,=-7,43082xlO-"A,3=-1,10638x10-2A,4=
-2,98267X10 A, 5= 2.96247xlO A , 6=-1,21161
1.44.201 x 10Ano= -2,5017
1X 10'Au+=-2,95133X10-'
AI+2: 8.69794X10-'Au3=
2.95233xlO' An4= -1,16804xlO-@Aos= 3
．． 02181X10-'Aoa=-8,25661X
10-'△1(10)=0.02529 △I(9)=0.01542 △+ (7)=0.00529 △+(5)=0.0O134 A211: -7,82587xlO-'A2G2 =-
1.57923X10-'A2+3= 1.4223
4xlO-'A214: 1.07694X10-'
A215: 1.53902X10-'A216:
-7,23157xlO-'△2(10)=-0,00
266 △2 (9) = 0.00069△2 (7)
= 0.00016△2 (5) = 0
．． 00003 Example 12 F = 1.0 R, = 0.68768 R2 = -2, 19402 NA = 0.50 D = 0.70969 W - D = 0.56434 β = O N = 1.57532 K, = 1 .67757XIO”A ,,=
-3,46061X 10-”A,, = -8,4
7761X 10-”A,, = -5,99075
XIO→A, 6=-1,81711XIO' A, 7= 6.61295xIO-'A,,=
1.73882X10O A,, = 1.69163X10' Aoo= -1,92578X10' A11l: -3,33521xtO-'AI+2 =
8.74426X10~6An3=2.910
32X10-'Au4=-1,57531X 10-
'Aoa= 4.11672XIO-'A+u= -
6,52422X 10-'N''R,' t=0.08871 Nt=1.510K 2=
-6,08502xlO'A23=-7,56380X10-'A24=3.
11476XIO-" A2. = -7,95033X 10-'A2.l
= 2,51097XlO'A2□=-3,7930
4xlO' A28= 3.02655X10°A 29= -4,40557X 10'Az+o=
-1,83521X 10 'A2++-= -6,
28316X 10-'A212= -1,58249
xlOzuA2+3=1.4.1389X10-'A2+
4: 1,29097X10-'A215: 1.
13129X10-'A2+s=-6,94110X
10-'NKI △1(10)=0.01200 △, (9)=0.01019 △+ (7)=0.00451 △+(5)=0.00121 △2(10)=0,00146 △ 2(9) =0.00153 △2(7) =0.00076 △2(5) =0.00017 Example 13 F = 1.0 R, = 0.68768 R2 = -2,06269 K, = 1 .82870X10-”A, 3=
-2,44392X 10-”A I4= -8,45
372xlO-”A,, = -9,34272x
10-”A, 6=-1,40660X10゜A1□=8.42223xlO-'A, 8=
1,18096X10゜A,, = 4.3695
0X10'NA=0.50 β=O D=0.77996 N=1.57531W・D
=0.52702 t=o, 08871 Nt=1.510K 2=
-6,00928X 10'A 23= -3,0
0087x 10-”A 2. = -1,40769
x 10-'A 25= -7,57093x 10-
'A 28= 3.97949 x 10゜A,
= −5,69922x lo 'A,, = 2.
65503X10゜A, = -4,61243x
10 'Aoo= 1.29290X10' Am= -3-31097xlO-' A112= 6.41128X10-'AI+3=
3.21519X10-'An4=-1,7844
2xlo-'Ao5= 4.08316xlOiAo6=-4,64873XIO-'A2+o=-
1,87730x io 'A2+1: -6,283
16x 10-'A212=-1,58258X10
-'A2+3= 1.42401 X 10-'A2
+4= 1.32498x 10-'A215=
1.38229X 10-'A2+a= -6,944
76X 10-'Δ1(10)=0.00079
△2(10)=0.00345△, (9)=0.006
21 △2(9)=0.00269△, (7)=0
．． 00387 △2(7)=O, 0O120△, (
5)=O,0O105△2(5)=O,0O034 Example 11 shown above. 12. In No. 13, the focal length F was 4.5 mm and the NA was 0.50. It is designed so that the thickness t of the parallel plate is 0.4 mm, and has imaging performance close to the diffraction limit within a field angle range of approximately 1°.

Further, the thickness t of the parallel plate has good imaging performance up to a variation of about ±0.1 mm under the conditions of the above NA and angle of view. That is, 0.065F<t<0. Good imaging performance can be obtained within the range of IIIF.

Example 11 described above. 12. 13, it is preferable that the following conditions (28) to (30) be satisfied in addition to the conditions (1) to (3) described above.

Conditions (28) and (29) are for properly correcting spherical aberration and coma aberration in the third-order region.

When the numerical value range of condition (28) is exceeded, the spherical aberration of the first surface in particular becomes large, and the aberration cannot be corrected completely by the aspherical term ψ of the first surface.

Condition (29) is a condition for correcting comatic aberration in a well-balanced manner on the second surface. If this value falls outside this numerical range, the aspherical term ψ2 of the second surface will not be able to fully correct the aberration, resulting in off-axis imaging. Performance deteriorates significantly.

Condition (30) is mainly a condition for satisfying the sine condition. In the present invention, off-axis aberrations within a certain range, especially comatic aberration, are well corrected as well as on-axis aberrations, but outside the range of condition (30), the isoplanatic condition is significantly lost, which is undesirable. It is something.

If the upper limit of the conditions is exceeded, the radius of curvature of the first surface will become too small, causing a large amount of negative spherical aberration, making it difficult to correct the aberration, and working distances W and D will become too short to be practical. For lenses that have the disadvantage of causing problems, the above-mentioned (1) to (3) and (28)
By satisfying the following conditions (31) to (34) in addition to the conditions (31) to (30), spherical aberration can be particularly well corrected.

(31) O<△, (10) <0.03F
(32) 0.0033F < △1 (7) <0.
006F(33) −0,005F< △2 (
10) <0.005F(34) 0 <
△2 (7) <0.002F From condition (31) (
34) is 100% of the effective diameter of the first and second surfaces of the lens, 7
This is the condition for determining the amount of aspherical surface in terms of %. By satisfying conditions (31) to (34), spherical aberration in particular can be corrected even better.

When the upper limits of conditions (31) and (32) are exceeded, the spherical aberration becomes excessive, and conversely, when it falls below the lower limits, the spherical aberration becomes under, and the axial performance deteriorates.

Conditions (33) and (34) mainly relate to correction of off-axis aberrations, and when the range is outside the upper and lower limits, the amount of coma aberration increases and off-axis performance deteriorates.

For different corrections of spherical aberration, (35) O<△+ (9) <0.02
F(36)O,0O05F <△, (5)
< 0.0O15F, for different corrections of coma aberration (37) - 0,001F < △2 (9)
<0.003F(38) O<△2(5)
It is preferable to satisfy the condition <0.0005F in addition to the conditions (1) to (3) and (28) to (30) described above.

Here, conditions (35) to (38) are conditions for determining the aspheric surface 1 at 90% and 50% of the effective system of the first and second surfaces of the lens.

Alternatively, in addition to the conditions (1) to (3) and (28) to (30) described above, it is preferable for aberration correction to satisfy the following condition (39).

If the lower limit of condition (39) is less than this, astigmatism will worsen, while if it exceeds the upper limit, coma aberration will remain, which is undesirable.

(Effects of the Invention) As described above, according to the present invention, an aspheric single lens with excellent aberration correction both on-axis and off-axis can be produced through a parallel plate having a thickness of approximately 0.04F to 0.11F. Can be provided.

In an optical head of an optical memory device such as an optical card recording/reproducing device, by employing the aspherical single lens according to the present invention as an objective lens or a collimator lens, it is possible to reduce the weight and size of the optical head.

[Brief explanation of the drawing]

FIG. 1 is a diagram showing a lens cross section of an aspherical single lens according to the present invention, FIG. 2, FIG. 3, FIG. 4, and FIG. 5. 6, 7, 8, 9, 10, 11, 12, 13, and 14 show examples of the aspheric single lens according to the present invention. FIG. 3 is a diagram showing spherical aberration, astigmatism, and distortion aberration. l ・・・・・・・・・・・・・・・・・・・・・・・・
・・・・・・・・・Aspherical single lens 2・・・・・・・・・
・・・・・・・・・・・・・・・・・・・・・Parallel plate D・・・・・・・・・・・・・・・・・・・・・・・・
・・・・・・・・・Lens thickness W-D・・・・・・・・・
・・・・・・・・・・・・・・・Working distance t・・・・・・
・・・・・・・・・・・・・・・・・・・・・・・・
・Thickness R,, R2 of parallel plate...
・Radius of curvature N, Nt of the first and second surfaces...
・・・・・・・・・Refractive index tA 3rd figure spherical convergence A cabinet convergence plan curve taomata difference. Figure 4 and Figure 5 A/A Figure 7 A Figure 8 A A

Claims (1)

[Claims] An aspherical single lens in which both the first and second surfaces are aspherical, and the aspherical surface defines the distance from any point on the aspherical surface to the tangent plane of the apex of the aspherical surface. , the distance from the arbitrary point to the optical axis is H, the standard radius of curvature of the νth surface is R_ν, the conic constant of the νth surface is K_ν, and the aspherical coefficient of the νth surface is A_ν_i.
(i = 3, 4, ...), it is an aspheric surface expressed by the following formula, and the following conditions (1), (2), (3
) is an aspherical single lens that satisfies the following. X=(H^2/R_ν)/[1+√{1-(1+K_ν
)(H/R_ν)^2}]+A_ν_3H^3+A_ν
_4H^4+... (ν=1, 2) (1) 0.70<(N-1)F^3/N^2R_1^3
<0.73(2)0.31<(N-1)D/NR_1<
0.51(3)-0.40<R_1/R_2<-0.2
7, where F is the focal length of the aspherical single lens, D is the thickness of the aspherical single lens on the optical axis, and N is the refractive index of the aspherical single lens with respect to the wavelength used.