JPH0345363B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a gradient index lens in which one or both end surfaces of a cylindrical transparent body whose refractive index changes continuously from the central axis toward the periphery are finished with a convex curved surface. . The refractive index n(r) at a point at a distance r in the radial direction from the central axis is approximately given by the square distribution formula of the following equation: n(r)=no[1-g ² /2r ² ] ...(1) The illustrated cylindrical transparent body is already well known as a focusing light transmitter. However, no is the axial refractive index,
g is a square distribution constant. When the length Zo of such a cylindrical optical transmitter is chosen as O<Zo<π/2g, its imaging characteristics are the same as a normal convex lens even though both end surfaces are flat, and it is The focal point is created at the position So=cot(gZo)/nog...(2) from the output end, and it is called a gradient index lens. However, the refractive index of an actual gradient index lens deviates from the square distribution of equation (1), and the fourth order of r,
It has higher-order aberration coefficients that are expanded in even powers of 6th order, . . . . Now, considering the aberration instead of formula (1) for the refractive index distribution, n ² (r) = n ² o [1 - (gr) ² + h4 (gr) ⁴ + h6 (gr) ⁶ ] ...(3) I will express it as Here, h4 and h6 are the fourth-order and sixth-order aberration coefficients, respectively. The focal point created by a lens body with such an aberration is (2)
In place of the formula, it is approximately located at S=Cot(ΩZo)/noutΩ...(4). However, Ω=g [1-3/4 (h4-2/3) (grin) ² - (15/16h6+15/64h4 ² +7/8h4-3/8)(gr
in) ⁴ ] ...(5) where nout is the refractive index at the output position, and rin is the distance from the central axis to the input position on the input end surface. As is clear from equation (5), in the case of a paraxial ray with a relatively small distance rin, Ω is approximately equal to g, but for a parallel ray incident at a position relatively far from the central axis, Ω≠ g, and △ at the above focal position
This results in a difference of S==S−So. Here, when the focal position created by the peripheral rays is farther from the focal position created by the paraxial rays with the exit end face as a reference, that is, the case where △S>O, is defined as positive axial aberration, and the opposite △ The case where S<O is defined as negative axial aberration. Whether ΔS is positive or negative depends on the composition of the base glass of the lens. For example, in molar percentage Na ₂ O (25-X), Tl ₂ OX, B ₂ O ₃ 15,
Glass with a composition of SiO ₂ 60 (this is called a type) and Na ₂ O (20−X), Tl ₂ OX, B ₂ O ₃ 20,
Glass with a composition of SiO ₂ 60 (this is called the type)
When two types of base metal rods were immersed in a potassium nitrate melt at 540°C and the progress of lens formation was observed over time by measuring the axial aberration, the X in Figures 1 and 2 was observed. As seen in the example of =10, it follows a completely different course. It was confirmed through experiments that when the lens formation was almost completed, as shown in Figure 3 a and b, △S>O for the type of glass lens, and △S<O for the type of glass lens. . FIGS. 4 and 5 show examples of the refractive index distribution of a type of gradient index lens having the characteristic of ΔS>O obtained from analysis of interference fringes using an interference microscope.

Zro=1.8mm, no=1.600, g=0.289mm ^-1 ,
h4 = 1.47, h6 = -30.5 are obtained, and if the refractive index distribution is drawn using these values, the ideal distribution of refractive index n(r) = no√
For sech (gr), as shown by the solid line in Figure 4, areas relatively close to the center are close to the ideal distribution or have a slightly large slope, while areas relatively far from the center to the periphery deviate from the ideal distribution. The slope is becoming gentler. Such characteristics are achieved when the composition of the lens glass is within a certain range of the type, in other words.
Only when h ⁴ and h ⁶ are within a certain value range, due to this characteristic, the focal point created by a parallel ray incident relatively near the center of the lens with length Zo < Zo < π/2g A focal point created by a parallel ray incident at a position relatively far from the center is connected to a point further away from the output end surface, and a circle of least confusion is formed between the points as shown in Figure 3. I can do it.
The present invention processes one or both end surfaces of the flat end surface of a gradient index lens having such positive axial aberration into a convex curved surface, and compensates for the positive value of the axial aberration, thereby reducing the axial aberration to zero. It is related to approaching , or converting it to a slightly negative value.

Theoretical calculations for reducing axial aberrations by making the end faces of gradient index lenses spherical have already been published.

However, as mentioned above, the spherical end face is useful for reducing aberrations only within a certain range of higher-order aberration coefficients of the refractive index distribution, and thus is effective only when the axial aberration takes a positive value. In some gradient index lenses, by processing the end face into a spherical shape, the axial aberration may be made larger than in the case where the end face is flat. For example, an example of measuring the characteristic values of a gradient index lens made by ion-exchanging a glass rod with a composition of x = 10 of the type described above is zro = 2.0 mm, no.
= 1.605, g = 0.294mm ^-1 , h4 = 6.6, h6 = -99
As shown in Fig. 5, the gradient of the refractive index near the center is a little gentler than the ideal distribution, but in the region relatively far from the center, the gradient of the refractive index is larger than the ideal distribution, as shown in Fig. 3. As shown in b, the focal point created by the parallel incident light ray relatively near the center of the input end face is compared to the focal point created by the parallel incident light ray relatively far from the center with respect to the output end face. (negative axial aberration) Therefore, spherical machining of the end face is not effective because it increases the value of the negative axial aberration.

The convex spherical finish on the end face is achieved by ion-exchanging a glass rod made from a certain limited range of composition near the glass composition of the type to obtain the 4th and 6th order aberration coefficients of the refractive index distribution expressed by equation (3). This is effective only for a gradient index lens whose both end faces are flat, which is obtained by controlling the angle so that it falls within the range shown in FIG.

Note that negative axial aberration can theoretically be made positive by making the end surface of a gradient index lens a concave curved surface, but general gradient index lenses used for video disc reading elements, etc. Polishing a concave curved surface is technically difficult because it is a small millimeter, and it is not practical because edge chipping is likely to occur.

And we determined that the molar percentage of SiO ₂ 57~
63%, _B2O3 12~18 _% , _Na2O13 ~22%, _Tl2O3 ~
If glass whose main component is 12% is used as the lens material, the axial aberration will always be positive as mentioned above.
Moreover, it has been found that aberrations can be almost completely corrected by forming the end face into a convex curved surface with a radius of curvature of about 1R to 10R (where R is the radius of the material rod), which is easy to polish.

In addition to the above-mentioned main components, the glass according to the present invention contains, for example, 4% or less ZnO, AS ₂ O ₃ or
There is no problem even if it contains subcomponents such as 0.5% or less of Sb ₂ O ₃ C.

When using the lens according to the present invention for reading or writing on a video disk, taking into account that the disk has positive axial aberration, the gradient index lens itself has a slightly negative axial aberration by controlling the curvature of the end surface. It is desirable to have a disk having an axial aberration of 1, and to compensate for this in combination with a disk having a positive axial aberration.

Example Na ₂ O 21%, Tl ₂ O 4%, B ₂ O ₃ 15 in molar percentage
%, SiO ₂ 60% glass was melted to produce a glass rod with a diameter of 2.0 mm. This was immersed in a potash nitrate melt maintained at 530°C, and the Tl+ ions in the glass were removed.
Na ⁺ ions are exchanged with K ⁺ ions, and the refractive index decreases continuously from the center to the periphery, and the parameters of the refractive index distribution are no = 1.553, g = 0.215 in 140 hours.
A gradient index lens with parallel planes on both end surfaces, expressed as mm ^-1 , h4 = 0.58, and h6 = 85, was obtained.

Using the above characteristic values, we calculated the focal position of the parallel rays incident at various positions on the end face using the ray tracing method and calculated the axial aberration. As a result, we found that there was a positive axial aberration as shown in Figure 7. was made into

Note that the vertical axis of the graph in FIG. 7 indicates the ratio between the lens radius R and the distance rin from the lens center axis to the light beam incident position.

The meandering pitch P of the light ray inside this lens is P=
Since 2π/g=29.22mm, the length of the lens is P/
When a parallel beam of wavelength λ = 0.63 μm is input from one end to 5.06 mm within 4, a spot with approximately Gaussian power distribution is formed at a position approximately 1.4 mm from the output end, and the power spreads by 1/e ² . was 2.2 μm, and the brightness of the lens at this time was NA = 0.34. Next, set the exit end of this lens to the radius of curvature ξ=3R=3×1
When a convex spherical surface was machined with =3 mm, the 1/e ² spread of the Gaussian-distributed emission spot was reduced to 1.4 μm, and the NA was increased to 0.41.

[Brief explanation of drawings]

Figure 1 is a graph showing the relationship between processing time and axial aberration △S when a lens material with the type of glass composition is subjected to ion exchange treatment. Figure 2 is a graph showing the relationship between the processing time and axial aberration ΔS when a lens material with the type of glass composition is subjected to ion exchange treatment. Graph showing the relationship between processing time and axial aberration △S, Figure 3a is a side view showing the aberration state of a gradient index lens due to different types of glass, Figure 3b is a graph showing the relationship between processing time and axial aberration ΔS, Figure 3b is a graph showing the relationship between processing time and axial aberration ΔS A side view showing the aberration state of a distributed type lens, Figure 4 is a graph showing the refractive index distribution type of a type glass lens, Figure 5 is a graph showing the refractive index distribution of a type glass lens, and Figure 6 is a graph showing refraction. FIG. 7 is a graph showing a desirable range of the fourth-order coefficient h4 and the sixth-order coefficient h6 of the index distribution, and FIG. 7 is a graph showing an example of the axial aberration of the lens material according to the present invention.

Claims (1)

[Claims] 1 mole percentage SiO ₂ 57-63%, B ₂ O ₃ 12-18%,
A cylindrical rod of glass whose main components are 13~22% Na ₂ O and 12% Tl ₂ O3 is ion-exchanged to give a refractive index distribution that changes in the radial direction from the central axis to the periphery. 1. A gradient index lens, characterized in that at least one end surface of a lens material that has positive axial aberration in a flat state is made into a convex spherical surface to correct the aberration or to create a slight negative aberration.