JPH0520722B2 - - Google Patents

Description

[Detailed description of the invention]

[Industrial Application Field] The present invention relates to a lens for micro-optics used in fields such as optical communications, optical computers, copying equipment, and medicine. [Prior art] In the past, graded index rod lenses (trade name: Cellhod lenses), conical lenses, and spherical lenses have been used as lenses for micro-optics in optical communication and copying equipment (for example, A.Nicaia App). .
Opt.20.P3136.1981). In addition, a lens in which a homogeneous sphere is embedded in the surrounding medium (for example, Japanese Patent Application Laid-Open No. 55-60912) and a two-layer tip spherical lens (for example, Japanese Patent Application Laid-Open No. 61-269107) have been proposed. (e.g. Iga et.al.Fundamental)
of Microoptics.Academic press.p127) was prototyped, and a lens with a spherically symmetric gradient index sphere embedded in a homogeneous surrounding medium (for example, Japanese Patent Application Laid-open No. 168026/1983, Y.Koike et.al.App.Opt.25.19). p3356.1986)
has been proposed and prototyped. There are ordinary convex lenses cut out from axially graded refractive index medium (same as this flat plate) (for example,
EWMarchand.Gradient Index Optics.
Academic press.p106). [Problems to be solved by the invention] For example, considering the use in a wavelength demultiplexer for optical communication, (a) spherical aberration is small. (b) The aberration at oblique axis incidence is small, that is, the sine condition is satisfied. (c) Optical elements such as interference filters, reflective films, and optical fibers can be closely integrated, and air spaces should be avoided as much as possible. (d) Can be used in adverse environments (high temperature, high humidity, dust, etc.). (e) It must be easy to manufacture. etc. are required. (a) is the core diameter of the single mode optical fiber (~10μ
(m) collimates the light flux from the optical fiber placed off-axis, and after traveling a certain distance, condenses it again and couples it to the optical fiber, increasing its efficiency; (b) collimates the light flux from the optical fiber placed off-axis. This is necessary for use as a so-called oblique-axis optical system, in which the light is reflected obliquely between parallel flat plates with reflective films and an interference filter, and then focused again on the end of an off-axis optical fiber. It is also necessary to loosen the transformer of fabrication and assembly. (C) reduces loss and at the same time strengthens the device and increases reliability. Table 1 shows the degree of satisfaction with items (a) to (e) for conventional lenses and compares them with the lens of the present invention. As a supplement to the comparison in Table 1, the requirements differ depending on the application, so for example, in the case of a lens for copying equipment, contrary to (c), an air layer must be added to make it lighter, and it must also be made to allow for movement. It won't happen. The lens of this invention can be used in either case by changing the thickness of the flat plate. Common requirements are (a) and (b) small aberrations, and (e) ease of manufacture, but there has been no conventional device that fully satisfies these requirements.

【table】

[Means for solving problems]

The first invention of the gradient index flat plate Sanderutsch type spherical lens according to the present invention is such that a concave spherical hole is formed in the surface of a flat plate whose refractive index changes at least near the surface in the thickness direction. A homogeneous sphere is sandwiched between the concave spherical surfaces in close contact with the concave spherical surface, and the change in the refractive index of the flat plate is set to a value that corrects the spherical aberration and coma aberration of the optical system. A second aspect of the gradient index flat plate Sanderuch type ball lens according to the present invention is that in the first aspect, the homogeneous sphere and the flat plate are made of a material that corrects chromatic aberration. [Operation] In the first aspect of the present invention, the spherical aberration caused by the homogeneous sphere is corrected by changing the refractive index applied to the flat plates that sandwich the homogeneous sphere. Furthermore, by distributing the refractive index change coefficients to both flat plates, coma aberration is prevented from occurring. Further, in the second aspect of the present invention, chromatic aberration is corrected by the materials of the homogeneous sphere and the flat plate. [Example] First, the principle of this invention is explained in Fig. 3 a~
This will be explained using c. In Figures 3 a to c, 1 is a homogeneous sphere (refractive index n _s ),
Acts as a lens. 2A, 2B are flat plates, 3A,
3B is a heterogeneous portion, and 4A and 4B are holes. In addition,
When it is not necessary to distinguish between A and B, simply use 2, 3, 4.
That's what it means. The same applies to other symbols described later. First, considering the imaging of a lens by a homogeneous sphere (refractive index n _s ) 1 placed in a homogeneous surrounding medium (refractive index n _b ), as shown in Figure 3a, a convex lens (n _s >
n _b ), the peripheral light of the luminous flux emitted from the object point O is focused in front of the image point I of the paraxial light, resulting in so-called negative spherical aberration. Therefore, in the present invention, similarly in the case of a convex lens (n _s >n _b ), as shown in FIG. Concave spherical holes 4A, 4 are formed on the surface, that is, on the high refractive index side.
B is opened, and by utilizing the fact that the difference in refractive index with the homogeneous sphere 1 that is in contact with it becomes smaller as the distance from the central axis increases, the peripheral light is focused near the image point I of the farther paraxial light,
Corrects spherical aberration. Furthermore, in order to eliminate comatic aberration that occurs when imaging an off-axis object point, two flat plate inhomogeneous parts 3A and 3B with different refractive index gradients according to the magnification of the optical system are provided on the input and output surfaces of the homogeneous sphere 1. The coma aberration generated on the input side is canceled out on the output side. For simplicity, 1:1
In the case of an optical system (magnification=-1), a qualitative explanation of its effect will be given. Inhomogeneous parts 3A and 3B with the same refractive index gradient are formed on the flat plates 2A and 2B on both sides of the homogeneous sphere 1, and three rays C ₁ from the object point O located above the optical axis in FIG. Consider C ₂ and C ₃ . As mentioned earlier, the difference in refractive index at the boundary becomes smaller as it moves away from the optical axis, so the upper ray C ₁ is refracted more by the second spherical surface S ₂ than by the first spherical surface S ₁ , and the lower ray C ₃ is It will be the opposite. Therefore, the upper ray C ₁ and the lower ray C ₃ can be made symmetrical about the center of the sphere. On the other hand, since the ray C ₂ passes through the center of the sphere and is symmetrical about the center of the sphere, the three rays C ₁ , C ₂ , and C ₃ are 1 on the image side.
They intersect at a point, and there is no coma aberration. In an optical system with an arbitrary magnification, Equation (31), which will be described later, is a corresponding conditional expression. Hereinafter, the operation of the present invention will be described quantitatively with reference to FIG. In Figure 2, 1 is a homogeneous sphere and C is the center of the sphere. The image formation formula of a spherical optical system is the basic formula for the νth surface with the spherical center C as the coordinate origin: 1/(N _i ′L _i ′) = (N _i ′−N _i ) /(N _i N _i ′r _i ) +1/(NiL _i ) +Δ _i (i=1, 2) ...(1) Δi= _N(i ′−N _i )/(2N _i ′ ² r _i )(1−r _i ² /L _{i Li} ′)×sin ² i _i ……(2) i _i ′=i _i+1 , N _i sini _i =N _i ′sini _i ′ ……(3) Here, N _i , N _i ′: i-th surface Left and right refractive index of the spherical boundary r _i : radius of curvature of the i-th spherical surface (r ₁ = R, r ₂ = -R) L _i , L _i ′: intersection point of the incident ray and refracted ray from the center of the sphere, respectively, and the optical axis Distance to i _i , i _i ′: Incident angle, refraction angle of i-th surface spherical boundary Let the refractive index of homogeneous sphere 1 be N ₁ ′ = N ₂ = n _s ……(4), and the refractive index distribution of the flat plate Let n(z) be a homogeneous part n(z)=n _b distribution part n(z)=n _b +γz/R ...(5). The concave spherical surfaces of the holes 4A and 4B drilled in the flat plate heterogeneous parts 3A and 3B (Fig. 3) are approximately z=y ² /
(2R), so for the sake of simplicity, if we assume that the depth of the distribution section is as deep as possible, the refractive index distribution at the cut end will be N ₁ = n _b for each of the input and output side flat plate heterogeneous sections 3A and 3B +α ₁ (h _s1 /R) ² N ₂ ′=n _b +α ₂ (h _s2 /R) ...(6) Here, h _s1 , h _s2 : Height of the input and output light at the spherical boundary α ₁ , α ₂ : Refractive index distribution coefficient at the cut end of the flat plate heterogeneous parts 3A and 3B on the input and output side (α = γ/2) The length of the perpendicular line drawn from the sphere center C to the extension line of the incident and output light to the homogeneous sphere 1 Assuming h ₁ and h ₂ ′, respectively, h _s1 (1+R/L ₁ ) h ₁ h _s2 (1−R/L ₂ ′) h ₂ ′ ……(7) Equation (1) is expressed in the homogeneous spherical system. Although this is the formula to be applied, it is expanded and used because the heterogeneous region is narrow.
Therefore, although the inhomogeneity is included in the refraction at the boundary, the bending in the medium must be compensated for separately. Imaging equation (8) is obtained using equations (1) to (7). R/L ₂ ′=R/f+R/L ₁ + [Σ _i=1,2 (C _GRi +C _GCi +C _PLANi +C _SPHERE ] (h ₁ /R) ² ...(8) Here, n _sb = n _s /n _b , f=(R/2)n _sb /(n _sb -1) ...(9) C _SPHERE = [3/n _sb -1-1/n _sb ² -R ² /(L ₁ L ₂ ′)] R/(2f) ...(10) C _GR1 =-α ₁ (1+R/L ₁ ) ³ /n _b C _GR2 =-α ₂ (1-R/L ₂ ′) ³ /n _b ...(11) C _GC j=0, C _PLAN j=0 (j=1, 2)...(12) Note that the coefficient of equation (12), which will be calculated later as a correction, is set to 0.
(C _GC j is the ray bending at the inhomogeneous portion, and C _PLAN j is the coefficient of aberration due to flat plate-air boundary refraction). Furthermore, assuming that the refractive index change in the inhomogeneous portion is δn<<n _b , h ₁ =h ₂ ' is approximated here. First, the light ray bending at the non-uniform part is corrected.
As shown in FIG. 4a, the optical axis is the z-axis and the y-axis is perpendicular to it, and a light ray in the y-z plane is considered. By integrating the ray equation, the conserved quantity shown in equation (13) is obtained. ncosθ=n _b cosθ _b ……(13) Light ray bending at the inhomogeneous part of the flat plate 2A on the incident side
Assuming that the change in height h _s1 from the optical axis can be ignored as an influence on L ₁ , using equations (13) and (7), δL _1GC = h _s1 (tanθ−tanθ _b ) = (L ₁ +R) δn/n _b ……(14) Here, δn=n(y=h _s1 )−n _b = α ₁ (h _s1 /R) ² ……(15) Furthermore, 1/(L ₁ + δL _1GC )= 1/L ₁ −δL _1GC /L ₁ ² ...(16) If we calculate the coefficient C _GC1 of equation (8) in the same way for the inhomogeneous part of the flat plate 2B on the output side, we get: C _GC1 = −α ₁ (R/L ₁ ) (1+R/L ₁ ) ³ /n _b C _GC2 = α ₂ (R/L ₂ ′) (1−R/L ₂ ′) ³ /n _b (17) Note that the signs of δL _1GC and δL _2GC ′ are positive if they give a positive aberration on the image side, and the magnitudes are the amount of aberration on the object side and image side, respectively. Furthermore, h ₂ ≒ h ₁ is assumed. The overall effect of the inhomogeneous part is added to the previous boundary refraction and becomes C _GRIN1 = C _GR1 + C _GC1 = -α ₁ (1 + R/L ₁ ) ⁴ /n _b CGRIN2 = C _GR1 + C _GC1 = -α ₂ (1- R/L ₂ ′) ⁴ /n _b ...(18) Next, when the object point O and the image point I are located outside the flat plates 2A and 2B, find the aberration term caused by the refraction of the flat plate plane (4th Figure b). Note that the length in air is expressed as a flat plate homogeneous part (n _b ) converted length. The aberrations of the incident and exit planes are δL _1PR = 0.5 (L ₁ + R + t ₁ ) (n _b ² /n _air ² −1) (h ₁ /L ₁ ) ² δL _2PR ′=−0.5 (L ₂ ′) −R −t ₂ ) (n _b ² /n _air ² −1) × (h ₂ ′/L ₂ ′) ² ...(19) The signs etc. are the same as in equation (17), and equation (8) ^Converting _{to the coefficient of _ _} ^_ _{_} ^_ _{_ 2} ′) ³ (1−R/L ₂ ′ −t ₂ /L ₂ ′)×(n _b ² /n _air ² −1) ……(20) Now that each element of aberration has been determined, Find the correction conditions. Spherical aberration correction condition; Σ _=1,2 (C _GRINi + C _PLANi ) + C _SPHERE = 0 ... (21) Atsube's sine condition; n _b sin u ₁ / (n _b sin u ₂ ') = β ... (22 ) As shown in FIG. 5, the paraxial light connects the boundary between the medium-equivalent air and the flat plates 2A and 2B with a straight line, whereas the peripheral light forms a broken line due to flat plate aberration.
If Equation (21) is satisfied and the spherical aberration is corrected, the object point O and the image point I are combined into one point. Since Equation (22) should hold true for real rays, that is, the quantities inside the flat plates 2A and 2B, the extension of the ray inside the flat plate,
In other words, the intersection of the extended broken line and the optical axis
Using L ₁ + δL _1PR and L ₂ ′−δL _2PR ′, the sine of equation (22) is sin u ₁ = h ₁ / (L ₁ + δL _1PR ) sin u ₂ ′ = h ₂ ′ / (L ₂ ′ −δL _2PR ′ ...(23) Also, the magnification β=L ₂ ′/L ₁ ...(24) h ₁ = h ₀ + δh ₁ , h ₂ ′=h ₀ +δh ₂ ′ ...(25) Substituting into equation (22), the sine condition is rewritten as the following equation: δh ₂ ′−δh ₁ = −h ₀ (δL _1PR /L ₁ +δL _2PR ′/L ₂ ′) ……(26) Heterogeneity The change in the direction of the light beam caused by the part is derived from the following equations for the incident side and the output side, respectively: δ (i ₁ - i ₁ ') = C _GRIN1 (h ₀ /R) ³ (1 + R/L ₁ ) δ(i ₂ −i ₂ ′)=C _GRIN2 (h ₀ /R) ³ (1 −R/L ₂ ′) ...(27) Also, the defining formula of h ₁ and h ₂ ′ is h ₁ = Rsin i ₁ , h ₂ ′=Rsin
Taking the differential of i ₂ ′ and assuming cos i≒1, δ(h ₂ ′−h ₁ )=Rδ(i ₂ ′−i ₁ ) ……(28) The relationship between the aberration coefficient and aberration in equation (8) is Using the equation equivalent to No. (16) shown, δL _1PR = −C _PLAN1 L ₁ ² h ₀ ² /R ³ δL _2PR ′=−C _PLAN2 L ₂ ′ ² h ₀ ² /R ³ ...(29) From equations (26) to (29), C _GRIN2 / (1-R/ ₂ ′) −C _GRIN1 / (1+R/L ₁ ) = C _PLAN2 / (R/L ₂ ′) + C _PLAN1 / (R/L ₁ ) ...(30) Solving equations (21) and (30) for α ₁ and α ₂ , α ₁ = W ₁ / (1 + R / L ₁ ) ³ , α ₂ = W ₂ / (1 - R / L ₂ ′) ³ ... (31)) Here, W = n _b (C _PLAN + C _SPHERE + Q =) / (2 - R / f) (λ = 1, 2) ... (32) C _PLAN = C _PLAN1 +C _PLAN2 Q ₁ = (1-R/L ₂ ′)P, Q ₂ =-(1+R/L ₁ )P P=C _PLAN1 / (R/L ₁ ) +C _PLAN2 / (R/L ₂ ′) ...(33) Next, conditions for chromatic aberration correction are derived. Paraxial light imaging formula 1/L ₂ ′=1/f+1/L ₁ is converted to length L ₁ =n _b t _1air −R−t ₁ , L ₂ ′=n _b t _2air +R+t ₂ ……(34 ), take the differentiation with respect to n _s and n _b , find the relationship between dn _s and dn _b that keeps the lengths in air t _1air and t _2air unchanged, and find the dispersion coefficient D _s = dn _s /dλ, D When expressed using _b = dn _b / dλ (λ is the wavelength in the optical wavelength band of interest), D _s /D _b = n _s /n _b [1-(R/2) (n _s /n _b ) × {(L ₂ ′−t ₂ −R)/L ₂ ′ ² −(L ₁ +t ₁ +R)/L ₁ ² }) ……(35) The relationship between the dispersion coefficient and Atsube number (μ) is as follows. It is given by Eq. D _s /D _b = (μ _b /μ _s ) (n _s −1) / (n _b −1)
...(36) The coefficients α ₁ and α ₂ that give the aplana take lens are shown in Figure 6 a and b, and the magnification β is set using n _s /n _b as a parameter.
shown against. The thickness of the flat plate on the optical axis is as shown in Figure 6a.
When t ₁ =t ₂ =R, FIG. 6b shows the case where the object point O and the image point I are inside the flat plate (including the surface) or at ∞. For example, assuming homogeneous sphere 1, n _s = 1.8, flat plate 2A,
Considering the case where parallel light is focused on the surface (β = 0) with a lens (n _s /n _b = 1.2) using a glass material with n _b = 1.5 as 2B, from Fig. 6b, α ₁ = 0.12,
α ₂ =0.41. If the incident height is used up to h _s1 /R=0.6, the refractive index difference of the inhomogeneous part of the flat plate 2A is α ₁
(h _s /R) ² = 0.043, the difference in refractive index of the inhomogeneous part of the flat plate 2B is that the output height is h _s2 /R = (1-R/f) (h _s1 /R),
Since R/f=1/3, α ₂ (h _s2 /R) ² =0.056
Both are about 5%, which is within the range that can be manufactured at present. In addition, in this example, numerical aperture NA=n _b (h _s1 /R)
(R/f)=0.3. Also, when the magnification β=-1, the flat plate thickness t ₁ = t ₂ = R,
Considering the same optical system as above, n _s and n _b are as shown in Figure 6a.
Therefore, α ₁ =α ₂ =0.22. When h _s1 /R=0.5 is used, a non-uniform portion with a refractive index difference of 0.055 is required. Next, a numerical example of chromatic aberration correction will be given. For flat plate material
Assuming n _b = 1.5 and n _s = 1.8 for the ball material, find the required Atsube number ratio μ _s / μ _b . Considering the convergence of parallel light, we set L ₁ ⇒∞, L ₂ ′=f in equations (35) and (36), and (μ _s /μ _b )=(1−1/n _s )/(1− 1/n _b )/[
1-(R/2)( _ns / _nb ) {(f- _t2 -R)/ ^f2 }]
...(37) When the image point I is set to the surface of the flat plate, that is, the thickness of the flat plate is t ₂ with f-t ₂ = R = 0, μ _s / μ _b = 1.333 …(38) Equation (38) is satisfied. For this purpose, a new glass material with a high refractive index and a high Atsbe number is required as the ball material. The above is for explaining the principle of this invention. Next, embodiments of this invention will be described. FIGS. 1a and 1b are a sectional view of a main part and a refractive index distribution diagram showing an embodiment of the present invention. In Figure 1a, 1 is a homogeneous sphere, 2A and 2B are flat plates,
In either case, near the surface on the opposing surface side, there are inhomogeneous parts 3A and 3B in which the refractive index changes in the thickness direction at least near the surface. Then, concave spherical holes 4A,
4B is formed, and the homogeneous sphere 1 is sandwiched between flat plates 2A and 2B from both sides in a sandwich-like manner so as to be in close contact therewith. The distribution of refractive index experienced by the light beam in this case is shown in FIG. 1b. This figure shows that the refractive index difference between the homogeneous sphere 1 and the hole surface is large, d ₁ and d ₁ ' for paraxial light, and d 2 and d _{1 '} for peripheral light.
This shows that d ₂ ′ is small (in the case of a convex lens). The differences between the lens of this invention and conventional lenses will be described. The lens of this invention has an axial refractive index distribution section 3A,
The cell hotter lens uses a rod radial distribution, the tip spherical lens and the spherical lens use homogeneous lenses, and the cells 2A and 2B use a spherically symmetrical refractive index distribution. is a normal convex lens cut out from an axial refractive index flat plate, and is the origin of the spherical aberration correction method.This invention is an advanced version of this correction method, and has improved its structure, effect, and function. That's different. That is, as shown in Table 1 above,
The differences are in the close integration with other optical elements, the ease of manufacturing as a microarray lens, and the increased freedom in material selection (for example, homogeneous spheres with a refractive index exceeding 2 can be used). Next, an example of application to a copying lens is shown in FIG. Assuming that the homogeneous spheres 1 corresponding to each layer are arranged coaxially, the condition for the luminous flux from the object point O to converge at the image point I in common for each axis is to satisfy the following relationship. . Relational expressions: f ₃ = Df ₁ , L ₃₄ = DL ₀₁ , L ₂₃ = DL ₁₂ , 1/
L ₁₂ = 1/f ₁ -1/L ₀₁ , f ₂ = L ₁₂ D/(1+D)
...(39) Here, the focal lengths of the first, second, and third layers are f ₁ ,
f ₂ , f ₃ , object plane and first layer, between the first and second layers, second,
The distances between the three layers and between the third layer and the image plane are respectively L ₀₁ , L ₁₂ ,
Let L ₂₃ , L ₃₄ and magnification be D. Note that here, the distance is expressed as an absolute value. In addition, the ratio of the spacing between the spherical centers C in each layer is determined by considering that the line segment connecting the points where the two optical axes cut the object plane and the image plane has an imaging relationship.
Regarding the 3 layers, 1+(1+D)/(2D)(L ₁₂ /L ₀₁ ): 1+L ₁₂ /L ₀₁
:1+(1+D)(L ₁₂ /L ₀₁ )/2...(40) However, the length is expressed in the flat plate medium conversion table. Now, when the distance between the object surface and the image surface is given as L ₀₄ in the medium conversion table, using the equation (39), L ₀₄ = (1 + D) (L ₀₁ + L ₁₂ ) ... (41) The actual length L _04R between the object surface and the image plane is given by A _IR as the actual air length, L _04R = L ₀₄ − (n _b −1) A _IR ……(42) To give a numerical example, D = 1.5. Magnifying lens L ₀₄
= 75mm and design using n _s = 1.8 and n _b = 1.5, f ₁ = 6.67, f ₂ = 6, f ₃ = 10, L ₀₁ = 20, L ₁₂ =
10, L ₂₃ = 15, L ₃₄ = 30, the ratio of the spacing between the spherical centers C is 1.42:1.5:1.625 for the first, second, and third layers, and the spherical radii are 2.22, 2, and 3.33, respectively. The unit is mm. As shown in Figure 7, in order to increase the transmittance,
It is desirable to use the homogeneous sphere 1 in the form of a drum.
Furthermore, from Fig. 7a, the coefficient of the flat plate inhomogeneity is 1st,
The values read at β=-0.5, -0.67, and -0.5 for the second and third layers, respectively, are used. Next, an example of application to a wavelength demultiplexer-multiplexer will be described. As shown in FIGS. 8a and 8b, the optical fiber 6 (frequency ν ₁ <ν ₂ <ν ₃ <ν ₄
<...) are obliquely coupled, and the diverging light from the optical fiber 6 is made into parallel light by the homogeneous sphere 1, passing through the flat plate surface (transparent part), and then by the mirror 9 on the second surface of the flat plate 5 pasted together. It is reflected, passes only the frequency ν ₁ wave by a low-pass filter or bandpass filter 8, and is focused into an optical fiber 6 ₁ by a second homogeneous sphere 1 ₁ . The remainder is reflected by a low-pass filter or band filter 8, and then reflected by a mirror 9 on the second surface of the parallel plate 5 (in addition, a mirror 7 on the first surface in FIG. 8a), and then transmitted to the next low-pass filter or band filter. 8 ₁ passes only the frequency ν ₂ wave and focuses it on the optical fiber 6 ₂ at the third homogeneous sphere 1 ₂ . The waves are separated in the same manner. If you trace it in the opposite direction, it becomes a multiplexer. The coefficient of the flat plate inhomogeneity of the lens used is
α ₁ was obtained by setting β=L ₂ ′/L ₁ =0 in Figure 6b,
α ₁ of α ₂ is the parallel light side, and α ₂ is the fiber side. Numerical example 1 In Figure 8a, n _s = 1.8, n _b = 1.5, β = 0,
α ₁ = 0.12, α ₂ = 0.41, f = 3R, the fiber side flat plate surface is -f when measured from the spherical center C, the positions of the filter side flat plate surface and the parallel flat reflecting mirror surface are not uniquely determined, but
Here, let them be f and 2f, respectively. The oblique axis angle from the optical axis of the fiber end is S/(4f), where the distance between the centers of the spheres is S, when the reflected light from the 2f plane is directed toward the adjacent sphere. If S = 2R, oblique axis angle: 0.17 rad, and the total width of parallel light is less than R, the fiber NA < R/
2/f=0.17, one side of the filter on the paper is R. The cutoff frequency of the filter should be ν ₁ < ν ₂ < ν ₃ < ν ₄ <
Decide between... R should be determined after the heterogeneous portions 3A and 3B of the flat plates 2A and 2B are prepared by ion exchange or the like and measured. This is because the coefficients are normalized by R as in equations (5) and (6). Numerical Example 2 This is a case where the thickness of the parallel plate 5 is doubled in Numerical Example 1, and the first surface of the parallel plate 5 is provided with only a filter without the mirror (FIG. 8b). first and second homogeneous spheres 1,
If the center spacing S ₁₂ of 1 ₁ is 2R, the oblique axis angle is R/
(3f) = 0.11 rad, the center spacing of the m-th, m+1 sphere (m>2) S _n,n+1 = (2/3) S ₁₂ = 1.33R, and the drum-shaped homogeneous sphere 1 with both sides cut off. Something is needed. That is, the homogeneous sphere 1 of the embodiment shown in FIG. 1 was spherical, but this is drum-shaped. Even in the case of a drum shape, the holes 4A and 4B in FIG. 1 have a concave spherical shape. Ray tracing example Figure 9 is a diagram of meridional rays near the image plane superimposed when the height of the object point from the optical axis is changed at equal intervals from 0 to R in an optical system with magnification β = -1. It is. FIG. 9a shows a case where there are heterogeneous parts 3A and 3B with coefficients α ₁ and α ₂ obtained from equation (31) and FIG. 6a.
For comparison, FIG. 9b shows a case where the non-uniform parts 3A and 3B are not present. It can be seen from this that the effects of this invention are clearly evident. In other words, a small spot can be obtained even if the image height is changed. Furthermore, what should be noted is that there is little curvature of field (good flatness). Utilizing this feature, it is suitable for the following applications. Diffraction grating wavelength demultiplexer Fig. 10a shows a wavelength demultiplexer using a single lens, and Fig. 10b shows a wavelength demultiplexer using a lens array. The wavelength-multiplexed light from the optical fiber 6 closely attached to one side of the flat plate 2A is collimated, reflected and diffracted by the diffraction grating 10 formed on the other flat plate surface in a direction corresponding to the wavelength, and passed through the lens again to the optical fiber 6, The signal is split into 6 ₁ , 6 ₂ , etc. In this case, even if the height of each fiber end from the optical axis is different, as mentioned above, the curvature of field is small, so the flat plate surface can be flat. Image Transmission Processing Lens Figure 11a shows a device for transmitting a flat image, which utilizes the flatness described above and can transmit high-quality images as they are. Optical fiber bundles are already in practical use for simple transmission, but they can also be used as image processing lenses that perform spatial filtering along the way. It can also include Fourier transform. Fiberscope head Figure 11b shows a fiberscope head typified by a gastrocamera. If the object surface is flat, the flatness of the image is good, so the end face of the fiber bundle 6' can be flat, and it is easy to manufacture a small head. [Effects of the Invention] As explained above, the first and second inventions according to the present invention include forming a concave spherical hole in the surface of a flat plate whose refractive index changes in the thickness direction at least near the surface; A homogeneous sphere is sandwiched between two flat plates in close contact with the concave spherical surface of the hole, and the change in the refractive index of the flat plate is set to a value that corrects the spherical aberration and sine condition of the optical system. The aberration is small even when the axis is used, and it can be integrated between ball lenses and other optical elements without intervening an air layer, so as can be seen from the example of the wavelength demultiplexer mentioned earlier, The device based on the ball lens according to this invention has low loss, high performance,
Furthermore, it is expected that it will be multifunctional and that tolerances for manufacturing and assembly will be relaxed. Further, since the inhomogeneous portion of the lens of the present invention functions to correct field curvature, it is suitable as an imaging lens, and has the advantage of contributing to medical care when used in a small fiberscope head. Further, the second aspect of the present invention also has the advantage of being able to eliminate chromatic aberration.

[Brief explanation of the drawing]

Figures 1a and 1b are block diagrams of an embodiment of the present invention;
Figure 2 is a definition of coordinates and parameters showing the relationship between lenses and light rays, Figure 3a is a diagram showing the spherical aberration of a sphere sandwiched between homogeneous flat plates, and Figure 3b is a flat plate with an inhomogeneous part. Principle diagram for correcting spherical aberration, Figure 3c
is a diagram explaining with a simple example the conditions for no aberrations to appear at the image point of an off-axis object point, Figure 4a is a diagram for determining the influence of ray bending in a non-uniform area, and Figure 4b is a diagram Diagram for determining aberrations due to refraction on a flat plate surface, 4th
Figure c shows the refractive index distribution of a flat plate, Figure 5 is a ray diagram for imposing the sine condition, and Figure 6 shows a and b the refractive index distribution coefficients of the flat plate on the input and output sides that satisfy the aplanatake lens condition. So, in Figure 6a, the flat plate thickness t ₁ = t ₂ =
In the case of R, Fig. 6b shows an example of application to a copying lens when the object point and image point are inside a flat plate, on the surface, or at ∞, and Fig. 8a and b show an example of a wavelength demultiplexer-combiner. Examples of application to wave instruments: Figure 8a is for a ball lens, Figure 8b is for a drum lens, and Figures 9a and b are for ray tracing to change the image height of a ray bundle near the image plane. Figure 9a is the case when the distribution coefficient of equation (31) is given, Figure 9b is the case when the coefficient = 0, Figure 10a, b
10A is a diagram of a diffraction grating wavelength demultiplexer, FIG. 10A is a diagram when a single lens is used, FIG. 10B is a diagram when a lens array is used, and FIG. 11A is a diagram of an example of application to an image transmission processing lens. , FIG. 11b is a diagram of an example of application to a fiberscope head. In the figure, 1 is a homogeneous sphere, 2A, 2B are flat plates, 3A,
3B is a heterogeneous part, 4A, 4B are concave spherical holes, 5
is a parallel plate, 6 is an optical fiber, 7 and 9 are reflecting mirrors,
8 is a low-pass filter or bandpass filter, 10 is a diffraction grating, O is an object point, and I is an image point.

Claims (1)

[Claims] 1. A concave spherical hole is formed in the surface of a flat plate whose refractive index changes at least near the surface in the thickness direction, and a concave spherical hole is formed between the two flat plates so that the concave spherical surface of the hole is closely connected. What is claimed is: 1. A gradient index flat Sanderch-type ball lens, characterized in that it has a configuration in which homogeneous spheres are sandwiched between the flat plates, and a change in the refractive index of the flat plates is set as a value for correcting spherical aberration and comatic aberration of an optical system. 2. The gradient index flat plate sanderch-type spherical lens according to claim 1, wherein the homogeneous sphere is a drum lens. 3. The refractive index distribution according to claim 1, characterized in that a plurality of concave spherical holes are formed on one side of the flat plate, and a plurality of homogeneous spheres are closely inserted into the holes. A flat sandwich type ball lens. 4. Drilling a concave spherical hole in the surface of a flat plate whose refractive index changes at least near the surface in the thickness direction, and sandwiching a homogeneous sphere between the two flat plates in close contact with the concave spherical surface of the hole. A gradient index flat plate sander circuit characterized in that the change in the refractive index of the flat plate is set to a value that corrects spherical aberration and comatic aberration of the optical system, and the homogeneous sphere and the flat plate are made of a material that corrects chromatic aberration. shaped ball lens.