JPS615220A - Refractive index distribution type single lens - Google Patents

Abstract

PURPOSE:To lengthen the working distance of a refractive index distribution type single lens by concaving the face of the lens on which liminous flux is incident with respect to object space and by also concaving the face of the lens from whih luminous flux is emitted with respect to image space. CONSTITUTION:When a single lens having a refractive index distribution in a direction perpendicular to the optical axis is used on reduction ratio, the face of the lens on which luminous flux is incident is concaved with respect to object space, and the face of the lens from which luminous flux is emitted is also concaved with respect to image space. The working distance is thus lengthened, and the spherical aberration and sine condition are corrected.

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a gradient index lens suitable for a collimator lens of a semiconductor laser, an objective lens for a pickup of an optical disk, and the like.

Conventional lenses with a refractive index distribution in the direction perpendicular to the optical axis, so-called radial gradient lenses - The Selfo Lens (trade name) is well known as an inch lens, and is an erecting equal-magnification imaging element. It is used in copying machines, etc. What are the advantages of gradient index lenses like this?

Although it is a single lens with flat end surfaces, it has relatively good performance and is suitable for mass production.

Taking advantage of these advantages, attempts have been made to use gradient index lenses as collimator lenses for semiconductor lasers and objective lenses for optical pickup.

For lenses used in such applications, a lens with a long working distance is desired. If a lens with a long working distance is constructed using a single gradient index lens with flat surfaces on both sides, The length d in the optical axis direction must be shortened. However, if the length d is shortened,
The gradient of the refractive index distribution in the direction perpendicular to the optical axis becomes steep, which not only makes manufacturing difficult, but also makes it impossible to satisfactorily correct aberrations.

In addition, when applying this type of lens, it is necessary to correct spherical aberration and sine condition well in terms of performance.
When using a radial gradient single lens, if both end surfaces are flat, spherical aberration and sine conditions cannot be corrected at the same time.

An object of the present invention is to provide a gradient index single lens with a long working distance.

A further object of the present invention is to provide a gradient index single lens that satisfactorily corrects both spherical aberration and sinusoidal conditions.

A further object of the present invention is that the Petz'R sum is small;
This provides a gradient index single lens with good off-axis characteristics.

In the gradient index single lens according to the present invention, when the single lens is used at a reduction magnification, the surface on the light beam incidence side is a gate to the object world side, and the surface on the light beam exit side is an image surface. The purpose is to achieve the above objective by making the surface a gate to the outside world. In addition, in this application, when used at reduced magnification,
The light flux incident side of the single lens is defined as the object world side, and the light flux exit side is defined as the image field side. The present invention will be explained in detail below.

In this specification, when the lens is used at a reduction magnification, the end surface on the object side is the first surface of the single lens, and the end surface on the image field side is the second surface. Therefore, when the single lens of the present invention is used as a collimator lens for a semiconductor laser, the surface on the semiconductor laser side is the second surface, and when it is used as a pink-up objective lens for an optical disk, the surface on the optical disk side is the MS2 surface. becomes.

In order to increase the working distance, it is effective to place a concave power on the object world side when used at reduced magnification. For this reason, in the single lens of the present application, the first surface is a surface concave toward the object world side.

Furthermore, the second surface also has a concave shape on the image field side, so that various aberrations are well corrected.6 Conventionally, in homogeneous lens systems, especially systems consisting of only a homogeneous single lens, the first surface is The reason for making the surface concave toward the object world is that if the first surface is a concave surface, the lens becomes larger than necessary.
It was considered undesirable because it was difficult to correct the negative spherical aberration that occurs on the surface; in particular, it was difficult to correct high-order spherical aberration. However, in the present invention, by using a medium having a refractive index distribution, the lens diameter does not become large even if the first surface is made a concave surface and a long working distance is taken. Furthermore, by giving the second surface a concave curvature toward the image field side, various aberrations can be effectively corrected. Furthermore, by satisfying appropriate conditions to be described later, more desirable aberration correction can be achieved.

In order to correct the spherical aberration and the sine condition, it is necessary to reduce the values of the third-order spherical aberration coefficient H and the coma aberration coefficient H.

When the refractive index N is the distance r from the optical axis, N (r)=N
□+N1 r20 N2r4+N5r6+−−−・−−
-(No, Nl, N2, N3------
In the radial gradient single lens expressed as (constant), the parameters that contribute to the value of the third-order aberration coefficient are N□, N1. N2 and rl: Radius of curvature of the first surface r2: Radius of curvature of the second surface d: Thickness. Among these, the axial refractive index NQ is 1.4 to 1.
Since it can only take a value of about 8, if we assume that N Q is 1.6, the parameters that contribute to the third-order aberration coefficient are rl, r2
．． d, N1. N2 (7) It is thought that there are five.

On the other hand, there are three required conditions, so even if rl is fixed, the condition (
r2. which satisfies A). d, N1. It is expected that there are many solutions to N2. Among these many solutions, one that can correct high-order aberrations or one that has an appropriate working distance can be selected according to the conditions of use.

r2. d, N1. Of N2, the three that contribute to the paraxial quantity are r2+cl and Nl, and Pj, 5an
Jour, Opt, Soc, Am, by ds, 60
．． As shown on pages 1436 to 1443 (1970), N2 has a linear relationship with each third-order aberration coefficient.

Therefore, for some rl and r2, condition (A)
d, N1. N2 can be determined by the following procedure.

(1) Give d arbitrarily.Ol) Find N1 so that the focal pressure #f of the single lens is constant.

(m) Find N2 so that I = O.

(iV)' Change d so that IT = 0 (
i) ~ (ii'i)
return .

Parameter r1. r2. d, N1
After determining the initial value of °N2, it is sufficient to balance each aberration by changing each parameter as in the case of conventional lens design.

Also, the higher-order coefficient N3 of the refractive index distribution. By introducing N4°, it is possible to further correct spherical aberration and increase the aperture.

The following facts became clear from the above design process.

First, regarding correction of spherical aberration and sine condition.

rl, r2. It is desirable that d satisfy the following conditions.

=2.7 ≦ f / r 1 ≦ −1,2 (1
)0 < f/r2≦2.9 (2) 1.3
≦ d'/f ≦ 4.5 (3
) f'/r1- exceeds the lower limit of conditional expression (1), the first
The surface becomes more concave, making it difficult to correct one spherical aberration.

Furthermore, if the upper limit of conditional expression (1) is exceeded, the effect of increasing the working distance and correcting aberrations due to the concave first surface cannot be obtained.

When f/r 2 exceeds the upper limit of conditional expression (2), the curvature of the second surface becomes strong, and the spherical aberration also worsens.

Note that the lower limit of conditional expression (2) is a value that is naturally determined depending on the shape of the second surface.

If d/f exceeds the lower limit of conditional expression (3), it is necessary to increase the slope of the refractive index distribution in order to maintain the focal length at f, making manufacturing difficult and worsening spherical aberration. Moreover, exceeding the upper limit of conditional expression (3) is not desirable from the point of view of practical miniaturization.

In order to satisfactorily correct the spherical aberration and the sine condition at the same time, it is desirable that the following conditions be satisfied.

Conditional expression (4) is an expression related to the power difference between the first surface and the second surface, and even if both the upper and lower limits of conditional expression (4) are exceeded, it is difficult to simultaneously correct the spherical aberration and the sine condition. become. That is, when the range of conditional expression (4) is exceeded, the comatic aberration difference, which is an asymmetric aberration, increases due to the power difference between the first surface and the second surface.

In order to perform better correction of spherical aberration and sine condition, 1
It is desirable that the following conditions be met.

If the lower limit of conditional expression (5) is exceeded, it becomes difficult to cancel out the spherical aberration generated by the two concave surfaces with the spherical aberration generated by the refractive index distribution, and if the upper limit of conditional expression (5) is exceeded, coma will also occur. The effect of aberration correction is lost.

Next, examples of the present invention will be shown. Table 1 shows lens data of the first to seventh embodiments according to the present invention, and the focal length of each lens is standardized to 1. Table 2 shows the pan-ink focus S'k, 3 when the object is at infinity for each example shown in Table 1.
The following spherical aberration coefficient I, coma aberration coefficient II, astigmatism coefficient m, Betsu'R sum P, distortion aberration coefficient V, This is a diagram showing the state of the refractive index distribution in Example 3, where the vertical axis shows the refractive index N and the horizontal axis shows the distance r from the optical axis. FIG. 3 shows various aberrations of the example.

Not only the single lens shown in the third embodiment but also other lenses have good performance with N and A of 0.3 and a half angle of view of about 3°. Especially the first one. Examples 3 to 7 have a small pevvr sum and have good angle of view characteristics for this type of lens.

In addition, as shown in Table 2, the third-order spherical aberration and coma aberration coefficient II have been well corrected, and when further increasing the aperture, higher-order refractive index distribution coefficients can be controlled. It is sufficient to correct the spherical aberration of .

Note that the third-order aberration coefficients in Table 2 and the aberration diagrams in FIG. 3 are calculated assuming that the object is at infinity and the entrance pupil is at the front principal point position.

In addition, in the embodiment, correction of spherical aberration is performed using a coefficient of refractive index distribution, N2. N3. . . . , but the same effect can also be obtained by introducing an aspheric surface to the first surface.

This is because for the third-order spherical aberration coefficient caused by the refractive index gradient, N2 is N2×f h3 (x) dx
.

For the third-order coma aberration coefficient, N2Xfh2 (x) h
(x) Contributes in the form of dx. Here h (x)
is the height of the paraxial ray at a point inside the heterogeneous medium,
h(x) is the height of the paraxial chief ray, and integration is performed in the optical axis direction of the heterogeneous medium. Therefore, these integral values are rt
It is determined only by +r2+d, No, Nt, the object, and the entrance pupil position, but if the entrance pupil is near the lens and the lens is not very long, h (x) is h (x)
The value is much smaller than that of N2, and N2 has almost no effect on the coma aberration coefficient. That is, the value of the coma aberration coefficient is rllr2. It is determined only by dlNo, N1 and object distance.

Although it is easy to obtain the effect of correcting the spherical aberration by N2 using the fourth-order aspherical coefficient of the first surface, the fourth-order aspherical coefficient does not contribute to the coma aberration coefficient in that case as well. At the stage where the spherical aberration is corrected, the coma aberration coefficient is not related to the entrance pupil position, so if the entrance pupil is located on the first surface, the contribution of the fourth-order aspherical coefficient to the coma aberration coefficient becomes zero.

This situation is basically the same for higher-order aberrations, so the coefficient of refractive index distribution N2°N3.・・・・・・
. . . are almost equivalent to the 4th order, 6th order, . . . aspherical coefficients in terms of aberration correction.

Furthermore, although the present invention aims to have good performance as a single lens, a single lens with spherical aberration corrected in this way is ideal for use in the most important parts of a combination lens system, such as the front lens of a photographic lens. Needless to say, it can be effectively used in locations where spherical aberration is likely to occur.

In addition, such a refractive index distribution has been achieved in the past by ion exchange methods, etc.
oike, Y, 0htsuka: Applied Opt
ics, 22, pp. 418-423 (1983), etc. can also be used.

As described above, the single lens according to the present invention has a long working distance and has well-corrected aberrations, and can be used as a collimator lens or an objective lens for picking up optical discs. Available for use.

[Brief explanation of the drawing]

Figure 1 is a diagram showing the shape of the single lens according to the present invention, Figure 2 is a diagram showing the refractive index distribution of the single lens shown in Figure 1, and Figure 3 is a diagram showing various aberrations of the single lens shown in Figure 1. Figure shown.

Claims (1)

[Claims] (1) In a single lens having a refractive index distribution in a direction perpendicular to the optical axis, when the single lens is used at a reduction magnification, the surface on the light flux incident side is relative to the object world side. The gradient index single lens (2) r_1 is characterized in that the surface on the light output side is concave with respect to the image field side, and the radius of curvature of the object field side end surface of the single lens is ,
If r_2 is the radius of curvature of the end surface on the image field side, d is the axial wall thickness, and f is the focal length, -2.7≦f/r_1≦-1.2 0<f/r_2≦2.9 1 .3≦d/f≦4.5 The gradient index single lens according to claim 1, wherein .3≦d/f≦4.5.