JPH0664229B2 - Gradient index rod / homogeneous convex compound lens - Google Patents

Description

The present invention relates to a gradient index lens used in an optical disc pickup system.

The operating gap (w
(1 to 2 mm) must be placed and focused on the back recording surface with a high numerical aperture (NA 0.45) through the thickness of the disc (d1.2 mm), and the lens diameter D must be a size corresponding to that. (If the total working distance l ₂ is l ₂ = w + d / nd, and nd is the refractive index of the disk, The commercially available objective lens is a set of 3 to 4 homogeneous spherical lenses, and it is an advantage that the diameter of the objective lens is set as large as necessary. However, on the other hand, the number of spherical surfaces is increased, so that there are drawbacks such that the precision of manufacture and assembly becomes strict.

In recent years, it has been proposed to apply a gradient index lens to reduce the number of lens surfaces and simplify an optical system. (For example, as a general-purpose lens, (1) DTMoore and PJSands, USPatent 3,729,253 For pickup, (2) K.Kikuchi et al.Appl.Opt.19,1076 (1980) (3) N.Yamamoto et al.Appl. Opt.21,1021 (1982) (4) K. Fujii et al. 4th Topical Meeting on Gradient−
index Opitical Imaging Systems. (5) Aono Proceedings of the 44th Annual Meeting of the Japan Society of Applied Physics 27P-
X-7., The 10th Micro Optics Workshop Lecture Paper Vol. NO.3 Octo
ber.1983 (The Japan Society of Applied Physics, Optical Society).

However, considering ion exchange, which is a viable means of forming a refractive index distribution in the glass rod, it takes time proportional to the square of the diameter of the glass rod, and long-time ion exchange makes the glass brittle and cracks occur. It is technically difficult to increase the diameter of the glass rod because it becomes easier. Therefore, it is desired to have a lens configuration in which the diameter of the glass rod is made as small as possible and the specifications of the pickup are satisfied.

According to the above-mentioned representative references (1) and (5), a so-called aplanate lens, in which spherical aberration and coma are corrected by a single lens, has its convex surface directed toward the light source when the light source is at a distance. It becomes a meniscus composition.

FIG. 1 shows an outline of a meniscus lens and a ray path. Since the lens power is concentrated on the first surface, the beam diameter emitted from the second surface becomes thin, and the working distance l ₂ × numerical aperture NA becomes small for the rod diameter. That is, the rod diameter is not effectively used.

In view of the above points, the present invention has been made for the purpose of eliminating the drawbacks of the conventional gradient index lens, and includes an axially symmetric gradient index rod (hereinafter referred to as a gradient index rod or simply a rod). The spherical lens is separated to move the power concentration position while maintaining the aplanate.

The present invention will be described below.

FIG. 2 is a schematic configuration diagram of a gradient index rod / homogeneous convex compound lens of the present invention. The gradient index rod 1 and the homogeneous convex lens 2 are combined so that the latter is located on the side of the disk 3, and the light source 4 is far away so that the magnification | β | <1.
The refractive index distribution n (r) of the rod is given by the following equation.

n ² (r) = n ² (0) [1- (gr) ² + h ₄ (gr) ⁴
+ H ₆ (gr) ⁶ ] (1) Here, n (0) is the refractive index of the central axis, g is the focusing parameter, and h ₄ and h ₆ are the 4th and 6th order coefficients. The ray path is slowly bent by the rod 1 and sharply by the homogeneous convex lens 2. As compared with the meniscus lens shown in FIG. 1, it can be seen that the beam diameter at the lens exit position is large and the product of the working distance and the numerical aperture can be increased.

Next, the spherical aberration and the sine condition (coma aberration) of this configuration lens
The correction will be described.

As shown in FIG. 3 (a), the spherical aberration of the homogeneous convex lens 2 is a so-called negative aberration in which peripheral light is coupled in front of paraxial light. In order to correct the aberration in combination with this, the gradient index rod 1 has at least positive aberration.

FIG. 3 (b) shows an outline of the light path in the gradient index rod in correspondence with the magnitudes of the distribution higher-order coefficients h ₄ and h ₆ . In terms of the path in the rod 1, h ₄ > h _{4 0} , h ₆ > h _{6 0} (h _{4 0} = 2/3, h _{6 0}
= -17/45), ambient light connects farther than paraxial light. That is, the aberration becomes positive. To qualitatively describe this reason, the main term of the refractive index gradient from the central axis of the rod 1 to the periphery [Equation ((1)] is differentiated by r and ∝-g ² r] is a fourth-order and sixth-order coefficient h ₄ , H ₆ is partially canceled by the increase of h ₆ , and the effect is greater as the distance from the central axis is further increased, so that the bending of marginal rays is reduced.

You will choose a rod with such a higher coefficient,
In the actual design and manufacture, the spherical curvature of the homogeneous lens is decided according to the refraction distribution obtained by measurement after rough control.

Details will be described later in an example of numerical calculation.

The correction of spherical aberration has been described above, but the correction of coma generated when the light source is off-axis is also important. This is because the pickup system uses a servo system to track the track, and it also has a meaning to loosen the tolerance of manufacturing the optical system.

FIG. 4 is a principle diagram of coma aberration correction.
(B), (c), and (d) qualitatively show how the coma aberration occurs due to the difference in the parameters of the gradient index rod 1 and the homogeneous spherical lens 2. The vertical arrows indicate the amount of imbalance in the magnitude of the change in direction due to the refraction of the upper and lower marginal rays that causes coma. The criterion is a virtual change in direction without coma aberration.

FIG. 4 (b) shows the case where the higher order term of the distribution is larger than the standard value,
As described above with respect to the spherical aberration, the light ray passing through the periphery of the rod 1 has a smaller change in direction, and an intersection of two peripheral light rays is formed outside the principal ray. That is, it is an outward coma aberration.

FIG. 4 (a) shows inward coma when the distribution higher order is smaller than the standard.

4 (c) and 4 (d) show a homogeneous spherical lens 2 and a disk 3.
In the system in which the spherical lenses are combined, the shape of the spherical lens shows the appearance of coma aberration in the case of meniscus and biconvex, respectively.

Now, in order to correct the coma aberration in the system in which the rod, the spherical lens and the disk are combined, the introverts shown in FIGS. 4 (a) and 4 (c) and the introversions shown in FIGS. 4 (b) and (d) are shown. It turns out that it is sufficient to join extroverts. (However, (a),
In (b), the direction of the light rays is reversed. If considering the original direction, the inward and outward directions are opposite.) It is possible to move the intersection point of the ambient light to the chief ray so that the image point shown in Fig. 4 (a) and (b) becomes a point light source. This is because the intersections shown in (c) and (d) of FIG.

In essence, as the higher order terms of the rod go from small to large, the homogeneous lens to be compounded moves from a meniscus to a biconvex lens.

Next, an example based on numerical analysis will be described. The parameters fixed by the optical system shown in FIG. 2 are set as shown in Table 1.

The rod length l and the distance l ₁ (−) from the lens surface to the light source are the parameters given in Table ₁ and the curvatures C ₁ and C _{2 of the} spherical surface.
(Reciprocal of curvature radii r ₁ and r ₂ and the sign is positive when the center of curvature is on the light exit side) is obtained from the relational expression of paraxial rays. However, since the curvatures C ₁ and C ₂ are the values finally obtained, it is assumed that the values start with a temporary value and are fed back to be converged. In addition, (-) means to treat as a negative amount in calculation. The path of an arbitrary light is obtained by applying the integral of the ray equation in the rod and Snell's law of refraction at the boundary surface to the given refractive index distribution of the rod.

Fig. 5 is a diagram showing a set of curvatures that make an aplanat for a given distribution higher order term. For a given 4th-order and 6th-order coefficient h ₄ = 0.8, h ₆ = 0.4 of the refractive index distribution, 6 shows the range of curvatures C ₁ and C ₂ that bring the lateral spherical aberration on the image surface within ± 1 μm. In addition, the three points P ₁ and P within the range are
₂ and P ₃ , the lateral spherical aberration curve and the sine condition dissatisfaction amount SCR × 100% defined by the equation (2) are shown.

SCR = (1 / β) (sin θi / sin θo-β) -SA / q
(2) Here, SA is the longitudinal spherical aberration, and q is the distance from the exit pupil to the image plane (for example, Yoshiya Matsui "Lens Design Method" Kyoritsu Publishing). The coma of a ray in the meridional plane is given by the product of SCR and image height. Therefore, for example, SCR x 100% = 0.2 (%)
In case of, the coma aberration of 0.4 μm occurs at the image height of 0.2 mm (the light source is off-axis 0.2 / | β | mm). It is understood that not only spherical aberration but also coma aberration can be reduced by selecting the curvatures C ₁ and C ₂ corresponding to the point P ₂ . So-called aplanat lenses are possible. The curvatures C ₁ and C ₂ are similarly searched by using the 4th-order and 6th-order coefficients h ₄ and h ₆ as other values to obtain the range of the 4th-order and 6th-order coefficients h ₄ and h ₆ that can be used by the aplanat lens. Figure 6 shows FIG. 6A shows a range in which the lateral spherical aberration is within ± 1 μm and the sine condition dissatisfaction amount SCR can be corrected so as to balance the positive and negative peaks. The solid line shows the contour line of the peak of the residual value of SCR x 100%. FIG. 11B shows the curvatures C ₁ and C ₂ to be selected for the _4th and 6th order coefficients h ₄ and h ₆ . As predicted using FIG. 4, as the fourth- and sixth-order coefficients h ₄ and h ₆ increase, the meniscus (C ₁ > 0, C ₂ > 0) becomes biconvex (C ₁
> 0, C ₂ <0).

FIG. 7 shows the required rod radii for the points on the center line of the region described in FIG. The rod diameter decreases as the fourth-order coefficient h ₄ increases.

For comparison, the dotted line shows the required rod radius when trying to satisfy the same specifications with only the rod.

The alternate long and short dash line shows the beam radius at the exit end.

As described above in detail, the gradient index rod / homogeneous convex compound lens of the present invention can be a lens in which spherical aberration and coma are corrected for a rod having a wide range of distribution coefficients. That is, it becomes easier to control the refractive index distribution of the rod,
Moreover, it has an excellent effect that the product of the working distance and the numerical aperture can be increased with a small rod diameter.

Further, there is an advantage that the structure can be simplified by reducing the number of spherical surfaces, and not only the cost can be reduced but also the reliability of the device can be improved.

[Brief description of drawings]

FIG. 1 is a diagram of a conventionally proposed meniscus lens, FIG. 2 is a schematic configuration diagram of a gradient index rod / homogeneous convex lens of the present invention, FIG. 3 is a principle diagram for correcting spherical aberration, and FIG. 4 is coma aberration. FIG. 5 is a diagram for explaining a set of curvatures that make an aplanat for a given distribution high-order term,
FIG. 6 (a) is a diagram for explaining the range of distribution higher-order terms that can be used as an aplanate and the amount of residual sine condition dissatisfaction, and FIG. 6 (b) is a diagram for explaining a set of curvatures to be selected for the higher-order terms. FIG. 7 and FIG. 7 are views for explaining the required rod diameter. In the figure, 1 is a gradient index rod, 2 is a homogeneous spherical lens, 3
Is a disc and 4 is a light source.

Claims (1)

[Claims] 1. In a compound lens of an axially symmetric gradient index rod and a homogeneous spherical lens, the refractive index distribution of the axially symmetric gradient index rod is expressed by the following formula (S1), and n ² (r) = n ² ( 0) [1- (gr) ² + h ₄ (gr) ⁴
+ H ₆ (gr) ⁶ ] (S1) (where n (0) is the refractive index of the central axis, and h ₄ and h ₆ are 4
Next, 6th order refractive index distribution coefficient, r is the distance from the central axis) Optical system magnification and focusing parameter, numerical aperture, spherical lens thickness and refractive index, which are items related to the configuration and parameters of the optical system, are inserted. Disc thickness and refractive index, working distance,
Given the distance between the rod and the spherical lens, and the rod length,
The distance from the lens surface to the light source is the first of the homogeneous spherical lenses,
When determined from the dihedral curvatures C ₁ and C ₂ , the spherical aberration is set as a target value for any one of the 4th and 6th order refractive index distribution coefficients (h ₄ and h ₆ ) measured after the rod is manufactured. The range of which the coordinates of the _first and second curvatures C ₁ and C ₂ of the homogeneous spherical lens to be corrected are calculated, and a range satisfying the sine condition within the target value is searched for, and a value determined from the common range Is the _first and second surface curvatures C ₁ and C _2. A gradient index rod-homogeneous convex compound lens.