Abstract:
A collimator lens meets conditions that: 
     (i) at least the outgoing surface is spherical; 
     (ii) the lens comprises at least an index-varying region in which the refractive index varies in the axial direction but does not vary in the direction perpendicular to the axial direction, and a constant index region all over which the refractive index is fixed; 
     (iii) the point having the maximum refractive index n oo  in the index-varying region is located at an apex of the profile of the lens; 
     (iv) when the refractive index n(Z) on the optical axis at a distance Z from the apex is represent by n(Z)=n oo  +n 1  Z+n 2  Z 2 , n oo  is within the range of 1.50 to 1.77, n 1  within the range of -0.14 to -0.02 mm -1  and n 2  within the range of -0.03 to +0.03 mm -2  ; and 
     (v) the inded-varying region is formed in the range of Z=0 to at least a depth d represented by an equation 
     
       d=D.sup.2 /{4R(1+√1-(D/2R).sup.2)} 
     
      where D is the aperture of the lens and R is the radius of curvature of the lens surface which includes the point having the maximum refractive index n oo .

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention: 
     This invention relates to a collimator lens which is useful to an optical system for reading from or writing in a recording medium. 
     2. Description of the Prior Art: 
     Recently, information processing using a high-density recording medium such as a compact disc, an optical disc or the like, has been rapidly advanced, in which an optical system is generally employed for reading from or writing in the recording medium. 
     In such an optical system, diffused light from a light source such as a semiconductor laser is converted to parallel rays by a collimator lens and then converged onto the surface of a recording medium by an objective lens. In addition to such an optical reading or writing system, a collimator lens has been generally and widely used for the purpose that diffused light is converted to parallel rays. When a collimator lens having reduced spherical aberration and coma is required, a compound lens consisting of plural spherical lenses has been used. In that case, however, it is hard to reduce the cost of the system. 
     In order to solve the above problem of such a compound lens system, system using an aspherical lens or a gradient index lens having refractive index gradient in the radial direction has been developed. Aspherical lenses are, however, unsuitable for mass-production because the aspherical surface is difficult to process or take an accurate measurement. On the other hand, a radial gradient index lens is made by an ion-exchange process of glass, however, the ion-exchange process has need of a long process time so that only a small lens having the effective aperture less than 5 mm can be obtained in practice. 
     SUMMARY OF THE INVENTION 
     Accordingly, it is an object of the present invention to provide a collimator lens which is suitable for an optical reading or writing system. 
     It is another object of the present invention to provide a collimator lens whose spherical aberration and coma can be reduced without remarkably increasing the cost. 
     It is still another object of the present invention to provide a method of making a collimator lens for an optical reading or writing system with facility for a relatively short time. 
     The above and other objects can be attained by the invention as follows. A collimator lens according to the invention meets conditions that: 
     (i) at least the outgoing surface is spherical; 
     (ii) the lens comprises at least an index-varying region in which the refractive index varies in the axial direction but does not vary in the direction perpendicular to the axial direction, and a constant index region all over which the refractive index is fixed; 
     (iii) the point having the maximum refractive index n 00  in the index-varying region is located at an apex of the profile of the lens; 
     (iv) when the refractive index n(Z) on the optical axis at a distance Z from the apex is represented by n(Z)=n 00  +n 1  Z+n 2  Z 2 , n 00  is within the range of 1.50 to 1.77, n 1  within the range of -0.14 to -0.02 mm -1  and n 2  within the range of -0.03 to +0.03 mm -2  ; and 
     (v) the index-varying region is formed in the range of Z=0 to at least a depth d represented by an equation 
     
         d=D.sup.2 /{4R(1+√1-(D/2R).sup.2)} 
    
      where D is the aperture of the lens and R is the radius of curvature of the lens surface which includes the point having the maximum refractive index n 00 . 
     The above collimator lens can be made by the following method. An oxide glass plate containing at least a kind of monovalent cations is brought into contact with a molten salt containing monovalent cations which are to serve to increase the refractive index of the glass material, and the cations of the molten salt are diffused into the glass plate so that an index distribution decreasing gradually from the surface to the inside of the glass plate is established to a predetermined depth and the deeper part than that depth remains a fixed refractive index, and subsequently, at least the surface of the glass plate at the side of the index-varying region is processed to a spherical surface. 
     Other further objects of the invention will become obvious upon an understanding of the illustrative embodiments about to be described or will be indicated in the appended claims, and various advantages not referred to herein will occur to one skilled in the art upon employment of the invention in practice. 
    
    
     BRIEF DESCRIPTION OF DRAWINGS 
     FIG. 1 is a sectional view of a collimator lens according to an embodiment of the invention; 
     FIG. 2 is a sectional view of a collimator lens according to another embodiment of the invention; 
     FIG. 3 is a graph showing a concentration distribution of Tl ions in a glass plate; 
     FIGS. 4A through 4F are aberration curves of lenses of examples 1 through 6 of the invention, respectively; 
     FIG. 5 is a graph showing a concentration distribution of Tl ions in a glass plate according to a different embodiment from that of FIG. 3; 
     FIGS. 6A through 6E are aberration curves of lenses of examples 7 through 11 of the invention, respectively; 
     FIGS. 7A through 7D are aberration curves of lenses of examples 12 through 15 of the invention, respectively; 
     FIG. 8 is a side view of an optical reading system for an optical disc in which a collimator lens of the invention is used; and 
     FIGS. 9A through 9D are views showing a process of making a collimator lens of the invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Hereinafter, embodiments of the invention will be described in detail with reference to attached drawings. 
     Referring first to FIG. 1, a collimator lens 1 has a first refracting surface 2A which is formed into a spherical surface having the radius of curvature R 1 . The refractive index n(Z) in the plane perpendicular to the optical axis 3 at a distance Z from the origin 0 which coincides with the central point of the spherical surface 2A, is represented by an equation 
     
         n(Z)=n.sub.00 +n.sub.1 Z+n.sub.2 Z.sup.2                   (1) 
    
     where n 00  is the refractive index at the origin 0, n 1  and n 2  are constants, and all of them are values in relation to the wavelength of a light source such as a semiconductor laser used in an optical system. 
     An index-varying region 1A having the above index distribution is formed in the thickness range of the origin 0 to a depth Z 0 . The refractive index is maximum at the origin 0 and decreases gradually as the distance Z increases. The values of n 00 , n 1  and n 2  fall within the ranges of 1.50 to 1.77, -0.14 to -0.02 mm -1  and -0.03 to 0.03 mm -2 , respectively. When the thickness of the lens is represented by t, the refractive index is fixed all over a region 1B in the thickness range of t minus Z 0 . The radius of curvature R 2  of a refracting surface 2B at the side of the constant index region 1B is determined so as to correct coma. The radius R 2  depends on the refractive index of the constant index region 1B and has a value within one of the ranges of 1/R 2  &gt;0, 1/R 2  =0 and 1/R 2  &lt;0. 
     In the lens 1, the distance S 0  on the optical axis between the central point 0 of the spherical surface 2A and the point corresponding to the outerest periphery of the sperical surface 24 is called &#34;sag&#34;. When the aperture of the lens is represented by D, the sag S 0  is given by an equation 
     
         S.sub.0 =D.sup.2 /{4R.sub.1 (1+√1-(D/2R.sub.1).sup.2)}(2 
    
     In this embodiment, the index gradient is established in the range of the central point 0 to the point distant from the central point 0 by a length Z 0  which is larger than the sag S 0 . 
     FIG. 2 shows another embodiment of the invention, in which an index-varying region 1A having the same index gradient as that of the embodiment of FIG. 1 is formed in the range of the central point 0 of one refracting surface 2A to a depth Z 0 , and another index-varying region 1C having index gradient represented by the above-mentioned equation (1) is formed in the range of the central point 0&#39; of the other refracting surface 2B to a depth Z 0  &#39;. A constant index region 1B is intermediate between them. Also in the region 1C, the distance Z 0  &#39; is larger than sag S 0  &#39; given by an equation 
     
         S.sub.0 &#39;=D.sup.2 /{4R.sub.2 (1+√1-(D/2R.sub.2).sup.2)}(3) 
    
     FIG. 8 shows an embodiment in which a collimator lens of the invention is used in an optical reading apparatus for an optical disc. Diffused light 5 emitted from a semiconductor laser 4 is introduced to a collimator lens 1 through a beam splitter 6. Parallel rays collimated by the collimator lens 1 are converged onto an optical disc 8 by an objective lens 7. Reflected light from the optical disc 8 is introduced through the objective lens 7, collimator lens 1 and beam splitter 6 to an optical detector (not shown). Alternatively, the beam splitter 6 may be disposed between the collimator lens 1 and the objective lens 7. 
     Next, a suitable method of making a collimator lens of the invention will be described with reference to FIGS. 9A through 9D. 
     An oxide glass plate 10 containing at least a kind of monovalent cations is used as a base material, which is dipped in a molten salt 11 at a temperature near the transition temperature of the glass as shown in FIG. 9A. The molten salt contains monovalent cations to increase the refractive index of the glass material, for example, at least a kind of cations selected from the group of Li ions, Cs ions, Tl ions and Ag ions. 
     In the dipping process, the cations of the molten salt are diffused into the glass plate from both surfaces thereof by ion-exchanging with the cations of the glass plate. As the result, as shown in FIG. 9B, an index distribution 12 decreasing gradually and evenly from the surface to the inside of the glass plate 10 is established by an ion concentration distribution. 
     Subsequently, as shown in FIG. 9C, a large number of disk-like lens materials 10A are cut from the glass plate 10. One or each of both flat surfaces of each lens material 10A is processed into a spherical surface having a predetermined radius of curvature so that the lens thickness is adjusted into a predetermined value. In the case that a single lens is formed from a single glass plate, if the above-mentioned dipping process is effected without masking the edge portion of a glass plate, an index distribution layer is formed also in the edge portion. In that case, it is preferable that processing to form a spherical surface is effected after removing the index distribution layer of the edge portion because the processing becomes easy in view of the change of the hardness of the surface to be processed. 
     A glass plate subjected to the above-mentioned ion-exchange process must contain at least a kind of monovalent cations and have a high refractive index within the range of 1.50 to 1.77. 
     For making a glass having a high refractive index, oxide such as TiO 2 , BaO, PbO and La 2  O 3  is generally used as an additive for increasing the refractive index. Those kinds of additives, however, may cause a change in quality of glass in the process of ion exchange or may lower the rate of ion exchange. In contrast to them, Tl 2  O is preferable because it can increase the refractive index by 0.010 to 0.015 per mole % without the above problems. 
     Tl ions are most preferable as cations contained by a molten salt for an ion-exchange process of the invention. As a molten salt, nitrate, sulfate, halide, etc. can be used. 
     The ion-exchange process of the invention is preferably effected at a temperature as high as possible because the ion-exchange rate increases in general as the temperature rises. Too high temperature, however, causes a deformation of glass. For these reasons, a temperature near the transition temperature of the glass to be processed is used in practice. Generally, the dipping process is preferably effected at a temperature within the range of the transition temperature plus or minus 50° C. 
     Hereinafter, experimental results will be described. 
     EXAMPLE 1 
     A disk-shaped glass plate having the diameter of 8 mm and the thickness of 3.2 mm was dipped in a molten salt at a temperature of 505° C. for 444 hours. The composition of the glass plate is shown in the following table 1. The molten salt consisted of 10 mole % Tl 2  SO 4 , 30 mole % K 2  SO 4  and 60 mole % ZnSO 4 . 
     
                       TABLE 1______________________________________Composition (weight %)   CharacteristicsSiO.sub.2B.sub.2 O.sub.3       ZnO    Na.sub.2 O                   K.sub.2 O                         Tl.sub.2 O                              Sb.sub.2 O.sub.3                                    Tg (°C.)                                           nd______________________________________39.2 4.1    19.0   7.2  5.5   24.8 0.2   478    1.600______________________________________ Tg: transition temperature 
    
     Tl ion concentration distribution in the thickness direction of the glass plate measured with an X-ray microanalyzer is shown in FIG. 3. 
     After grinding each flat surface of the glass plate by a thickness of 0.1 mm, the index distribution in the thickness direction was measured. The result showed an index distribution which evenly and equally descends from each flat surface to a depth of 0.8 mm. The refractive index at each flat surface was 1.641. The index distribution from each flat surface to the inside of the glass plate in the range of 0≦Z≦0.8 mm was given by n(Z)=1.641-0.0514Z. 
     The refractive index in the intermediate region between both index-varying regions in the thickness range of 1.4 mm was not changed by the ion-exchange process and had a constant value 1.600 which was the same as that of the original glass material. 
     Subsequently, both flat surfaces of the glass plate were ground to spherical surfaces having the radii of curvatures of R 1  =7.90 mm and R 2  =-249.8 mm, respectively, so that the aperture of the lens was adjusted to 7.2 mm. 
     The focal length and numerical aperture (NA) were 12.0 mm and 0.3, respectively. A measurement result of spherical aberration (on the axis) of this optical system is shown in FIG. 4a. The maximum spherical aberration and coma of this system were 2 μm and less than 5 μm, respectively. 
     EXAMPLES 2 TO 6 
     Glass materials having different refractive indexes were provided. Each of them was subjected to an ion-exchange process fundamentally similar to that of Example 1. As the result, lens materials having various index distributions in the thickness directions were obtained. Each lens materal was then processed to form spherical surfaces. Index distributions mesured and conditions of lenses finally obtained are shown in the following tables 2A and 2B, respectively. 
     
                       TABLE 2A______________________________________Ex-   Distance Z (mm)ample on the axis  Index distribution______________________________________2       0˜0.4              n(Z) = 1.556 - 0.138Z - 0.00513Z.sup.2 0.4˜2  n(Z) = 1.503       0˜0.4              n(Z) = 1.650 - 0.124Z 0.4˜1.6              n(Z) = 1.6 1.6˜2.0              n(Z) = 1.6 + 0.124(Z - 1.6)4       0˜0.15              n(Z) = 1.608 - 0.0514Z 0,15˜2 n(Z) = 1.65       0˜0.4              n(Z) = 1.687 - 0.0297Z 0.4˜2  n(Z) = 1.6756     0˜1    n(Z) = 1.631 - 0.0309Z 0˜3    n(z) = 1.6______________________________________ 
    
     
                       TABLE 2B______________________________________                                      FocalEx-   R.sub.1 R.sub.2   t     D      NA    lengthample (mm)    (mm)      (mm)  (mm)   (mm)  (mm)______________________________________2     3.23     -13.76   2     3      0.3    53     3.42     -50.85   2     3      0.3    54     7.56    -181.40   2       2.4  0.1   125     13.19    303.66   2     6       0.15 206     12.82   -694.13   3     10      0.25 20______________________________________ 
    
     Spherical aberrations of the lenses are shown in FIGS. 4B through 4F, respectively, and other characteristics are shown in the following table 3. 
     
                       TABLE 3______________________________________         Maximum spherical                       comaExample       aberration (μm)                       (μm)______________________________________2             0.3           0.43             0.7           1.54             0.1           0.35             0.1           0.86             0.6           4______________________________________ 
    
     EXAMPLE 7 
     A disk-shaped glass plate having the diameter of 10 mm and the thickness of 1.6 mm was dipped in a molten salt at a temperature of 472° C. for 500 hours. The composition of the glass plate is shown in the following table 4. The molten salt consisted of 5 mole % Tl 2  SO 4 , 40 mole % K 2  SO 4  and 55 mole % ZnSO 4 . The transition temperature (Tg) of the glass was 490° C. 
     
                       TABLE 4______________________________________Composition (weight %)   CharacteristicsSiO.sub.2B.sub.2 O.sub.3       ZnO    ZrO.sub.2                   Na.sub.2 O                         K.sub.2 O                              Tl.sub.2 O                                    Tg (°C.)                                           nd______________________________________37.2 4.0    18.3   2.0  5.7   4.9  27.9  490    1.621______________________________________ 
    
     Tl ion concentration distribution in the thickness direction of the glass plate measured with an X-ray microanalyzer is shown in FIG. 5. 
     After grinding each flat surface of the glass plate by a thickness of 100 μm, the index distribution in the thickness direction was measured. The result showed an index distribution that the refractive index n(Z) on the optical axis at a distance Z from one flat surface was given by n(Z)=1.638-0.034Z in the range of Z=0 to 500 μm, n(Z)=1.621 (constant) in the range of Z=500 to 900 μm and n(Z)=1.621+0.034Z in the range of Z=900 to 1400 μm. 
     Subsequently, one flat surface of the glass plate was processed into a spherical surface having the radius of curvature R 1  =10.84 mm and the aperture of the lens is adjusted to 4.76 mm. The focal length of the lens obtained, which had a spherical surface at one side and a flat surface at the other side, was 17.0 mm and the numerical aperture NA thereof was 0.14. 
     The lens was arranged so that parallel rays enter from the spherical surface into the lens. A beam splitter made of an optical glass BK7 and having the thickness of 5 mm was disposed in the rear of the lens. When the working distance WD is defined by (distance between the outgoing surface and the focal point) minus (thickness of the beam splitter), WD was 12.77 mm. 
     A measurement result of spherical aberration (axial aberration LSA) of this optical system is shown in FIG. 6A. The maximum hight of image was 0.6 mm and the third-order plus fifth-order coma was less than 4 μm. 
     EXAMPLES 8 TO 11 
     Glass materials having different refractive indexes were provided. Each of them was subjected to an ion-exchange process similar to that of Example 7. As the result, lens materials having various index distributions in the thickness directions were obtained. Then, lenses were made from the lens materials, respectively. Index distributions in the lenses measured and conditions of the lenses are shown in the following tables 5A and 5B, respectively. Each lens had a spherical surface having the radius of curvature R at the side of higher refractive index and a flat surface at the other side. In Example 8, a sufficiently thick glass plate was subjected to an ion-exchange process and then the surface portion was cut for a sampling lens from the glass plate. In Example 10, a glass plate having the thickness of 2 mm was subjected to an ion-exchange process for a long time so that both index-varying regions formed by ion-diffusing might intercross to each other. 
     
                       TABLE 5A______________________________________  Distance Z (mm)Example  on the axis  Index distribution______________________________________ 8       0˜0.5               n(Z) = 1.68 - 0.0345Z  0.5˜1.5               n(Z) = 1.663 9       0˜0.5               n(Z) = 1.635 - 0.041Z + 0.040Z.sup.2  0.5˜1.0               n(Z) = 1.624  1.0˜1.5               n(Z) = 1.624 + 0.021(Z - 1)10       0˜1.0               n(Z) = 1.66 - 0.034Z  1.0˜2.0               n(Z) = 1.625 + 0.034(Z - 1)11       0˜0.5               n(Z) = 1.627 - 0.041Z  0.5˜1.0               n(Z) = 1.606  1.0˜1.5               n(Z) = 1.601 + 0.041(Z - 1)______________________________________ 
    
     
                       TABLE 5B______________________________________Lens conditionsExample  R (mm)   t (mm)  D (mm) NA (mm)  Fl (mm)______________________________________ 8     11.56    1.5      4.76  0.14     17.0 9     10.80    1.5     5.5    0.16     17.010     11.88    2.0     5.4    0.15     18.011      9.40    1.5     5.7    0.19     15.0______________________________________ 
    
     Each lens obtained was evaluated with an optical system shown in the following table 6. Spherical aberrations of the lenses are shown in FIGS. 6B through 6E and other characteristics are shown in the table 6. In the table 6, &#34;BS&#34; represents a beam splitter made of BK7 glass and having the thickness of 5 mm. 
     
                       TABLE 6______________________________________Ex-                      Maximum    Coma ofam-  Optical system for  height of  3rd plusple  measurement         image (mm) 5th order______________________________________ 8   with BS   WD = 12.79 mm 0.6      less than 2 μm 9   with BS   WD = 12.81 mm 0.6      less than 10 μm10   without BS          WD = 16.78 mm 0.6      less than 1 μm11   without BS          WD = 14.07 mm 0.6      less than 7 μm______________________________________ 
    
     EXAMPLE 12 
     A disk-shaped glass plate having the diameter of 16 mm and the thickness of 10.5 mm was dipped in a molten salt at a temperature of 525° C. for 45 days. The composition of the glass plate is shown in the following table 7. The molten salt consisted of 22 mole % TlNO 3  and 78 mole % KNO 3 . 
     
                                           TABLE 7__________________________________________________________________________Composition (weight %)     CharacteristicsSiO.sub.2   B.sub.2 O.sub.3 ZnO    Na.sub.2 O       K.sub.2 O          Tl.sub.2 O             Sb.sub.2 O.sub.3                 Al.sub.2 O.sub.3                      Tg (°C.)                               nd__________________________________________________________________________39.1   2.1 19.0    7.2       5.5          24.8             0.2 2.1  485      1.600__________________________________________________________________________ 
    
     Tl ion concentration distribution in the thickness direction of the glass plate measured with an X-ray microanalyzer was the same as that of FIG. 3. 
     After grinding each flat surface of the glass plate by a thickness of 0.1 mm, the index distribution in the thickness direction was measured. The result showed an index distribution which evenly and equally descends from each flat surface to a depth of 2.1 mm. The refractive index at each flat surface was 1.724. The index distribution from each flat surface to the inside of the glass plate in the range of 0≦Z≦2.1 mm was given by n(Z)=1.724-0.0600Z. 
     The refractive index in the intermediate region between both index-varying regions in the thickness range of 6.1 mm was not changed by the ion-exchange process and had a constant value 1.600 which was the same as that of the original glass material. 
     Subsequently, the glass plate was cut and separated at the center of the thickness parallel with both flat surfaces so that two glass plates having the same index distribution were obtained. Then, the surface at the side of index-varying region of each glass plate was processed into a spherical surface having the radius of curvature R 1  =7.24 mm and the other surface thereof remained flat. The thickness and aperture of each lens were adjusted to 4.5 mm and 10.0 mm, respectively. The focal length and numerical aperture (NA) of each lens obtained were 10.0 mm and 0.5, respectively. 
     A measurement result of spherical aberration (axial aberration) of this optical system is shown in FIG. 7A. The maximum spherical aberration and coma of this system were 4 μm and less than 15 μm, respectively. 
     EXAMPLES 13 to 15 
     Glass materials having different refractive indexes were provided. Each of them was subjected to an ion-exchange process fundamentally similar to that of Example 12. As a result, lens materials having various index distributions in the thickness directions were obtained. In Examples 13 and 14, each disk-shaped glass plate after an ion-exchange process was cut at the center of the thickness similarly to that of Example 12, subsequently, the surface at the side of the index-varying region was processed into a spherical surface and the surface at the side of the constant index region was polished to remain a flat surface. In Example 15, both surfaces of a disk-shaped glass plate after an ion-exchange process were processed into spherical surfaces. 
     Index distributions in the lenses measured and conditions of the lenses are shown in the following tables 8A and 8B. In the table 8A, Z represents the distance from the origin which is the intersecting point between the outgoing surface and the optical axis, toward the inside of the lens. 
     
                       TABLE 8A______________________________________Example Z (mm)    Index distribution______________________________________13      0˜1.6             n(Z) = 1.765 - 0.0573Z   1.6˜5.1             n(Z) = 1.67514      0˜0.6             n(Z) = 1.583 - 0.135Z - 0.00554Z.sup.2   0.6˜2.2             n(Z) = 1.515      0-2.7     n(Z) = 1.684 - 0.0314Z   2.7˜9.2             n(Z) = 1.6   9.2˜11.9             n(Z) = 1.6 + 0.0314(Z - 9.2)______________________________________ 
    
     
                       TABLE 8B______________________________________  R.sub.1 R.sub.2  t     D      NA    FlExample  (mm)    (mm)     (mm)  (mm)   (mm)  (mm)______________________________________13     7.42     149.8   5.1   9      0.45  1014     3.33     -14.92  2.2   3.5    0.35   515     14.6    -137.0   11.9  16     0.4   20______________________________________ 
    
     Spherical aberrations of the lenses obtained are shown in FIGS. 7B through 7D, respectively, and other characteristics are shown in the following table 9. 
     
                       TABLE 9______________________________________        Maximum spherical                      comaExample      aberration (μm)                      (μm)______________________________________13           2             814           1             115           10            10______________________________________ 
    
     According to the invention, a lens material can be obtained by such a simple manner that a glass plate is subjected to an ion-exchange process in a molten salt, so that, a highly efficient collimator lens with low spherical aberration and coma can be obtained by the manner that the lens material is only processed to have a spherical surface or surfaces.