Graded refractive index lens system

Claim 2

A graded refractive index lens in which the refractive index n at the radial distance r from the optical axis is expressed by the formula shown below on the premise that n 0 represents the refractive index on the optical axis of said lens, n 1 , n 2 , . . . respectively represent the 2nd-, 4th-, . . . order coefficients: n=n.sub.0 +n.sub.1 r.sup.2 +n.sub.2 r.sup.4 +. . . and in which the shapes of both an incident side refracting surface and an exit side refracting surface of said lens have positive refracting powers and at least said incident side refracting surface is aspherical and is expressed by equation (A) shown below, and said graded refractive index lens satisfies the following conditions (1), (2) and (3): ##EQU2## 0<(n.sub.0 -1)f/r.sub.1 <0.4 (1)

Claim 3

38<-(n 0 -1)f/r 2 <0.65 (2) -0.3<n.sub.1 f.sup.2 <-0.1 (3) where C represents the curvature of the vertex portion of said aspherical surface, P represents the constant of cone, E, F, G, . . . respectively represent the 4th-, 6th-, 8th-, . . . order coefficients of r, r 1 represents the radius of curvature of the incident side refracting surface of said lens, r 2 represents the radius of curvature of the exit side refracting surface of said lens and f represents the focal length of said lens.

Claim 4

38<-(n 0 -1)f/r 2 <0.65 (2) -0.3<n.sub.1 f.sup.2 <-0.1 (3) where C represents the curvature of the vertex portion of said aspherical surface, P represents the constant of cone, E, F, G, . . . respectively represent the 4th-, 6th-, 8th-, . . . order coefficients of r, r 1 represents the radius of curvature of the incident side refracting surface of said lens, r 2 represents the radius of curvature of the exit side refracting surface of said lens and f represents the focal length of said lens.

Claim 5

A graded refractive index lens according to claim 1, further satisfying the following condition: 0.6<-r.sub.1 /r.sub.2

Claim 6

A graded refractive index lens according to claim 1, further satisfying the following condition: |n.sub.0 n.sub.2 /4n.sub.1.sup.2 |<1000

Claim 7

A graded refractive index lens according to claim 1, said incident side refracting surface being an aspherical surface, wherein said graded refractive index lens has the following numerical data: ______________________________________ f = 1.0 NA = 0.47 IH = 0.0217 WD = 0.384 r.sub.1 = 1.329 d = 1.184 n.sub.0 = 1.5 n.sub.1 = -0.18845 r.sub.2 = -1.026 n.sub.2 = 0.48548 × 10.sup.-1 P.sub.1 = -0.0617 E.sub.1 = 0.33929 × 10.sup.-2 F.sub.1 = -0.15788 G.sub.1 = -0.53064 (n.sub.0 - 1)f/r.sub.1 = 0.38 (n.sub.0 - 1)f/r.sub.2 = -0.49 -r.sub.1 /r.sub.2 = 1.30 |n.sub.0 n.sub.2 /4n.sub.1.sup.2 | = 0.51 ______________________________________

Claim 8

A graded refractive index lens according to claim 1, said incident side refracting surface being an aspherical surface, wherein said graded refractive index lens has the following numerical data: ______________________________________ f = 1.0 NA = 0.47 IH = 0.0217 WD = 0.350 r.sub.1 = 1.492 d = 1.268 n.sub.0 = 1.5 n.sub.1 = -0.21592 r.sub.2 = -1.105 n.sub.2 = 0.14707 × 10.sup.-1 P.sub.1 = 0.8407 E.sub.1 = -0.5045 × 10.sup.-1 F.sub.1 = -0.11761 G.sub.1 = -0.41134 (n.sub.0 - 1)f/r.sub.1 = 0.34 (n.sub.0 - 1)f/r.sub.2 = -0.45 -r.sub.1 /r.sub.2 = 1.35 |n.sub.0 n.sub.2 /4n.sub.1.sup.2 | = 0.12 ______________________________________

Claim 9

A graded refractive index lens according to claim 1, said incident side refracting surface being an aspherical surface, wherein said graded refractive index lens has the following numerical data: ______________________________________ f = 1.0 NA = 0.47 IH = 0.0217 WD = 0.407 r.sub.1 = 1.948 d = 1.334 n.sub.0 = 1.65 n.sub.1 = -0.16637 r.sub.2 = -1.212 n.sub.2 = 0.19035 × 10.sup.-1 P.sub.1 = -0.8319 E.sub.1 = -0.64927 × 10.sup.-1 F.sub.1 = -0.13994 G.sub.1 = -0.30808 (n.sub.0 - 1)f/r.sub.1 = 0.33 (n.sub.0 - 1)f/r.sub.2 = -0.54 -r.sub.1 /r.sub.2 = 1.61 |n.sub.0 n.sub.2 /4n.sub.1.sup.2 | = 0.28 ______________________________________

Claim 10

A graded refractive index lens according to claim 1, said incident side refracting surface being an aspherical surface, wherein said graded refractive index lens has the following numerical data: ______________________________________ f = 1.0 NA = 0.47 IH = 0.0217 WD = 0.425 r.sub.1 = 2.304 d = 1.409 n.sub.0 = 1.75 n.sub.1 = -0.14698 r.sub.2 = -1.318 n.sub.2 = 0.15155 × 10.sup.-1 P.sub.1 = 1.0795 E.sub.1 = -0.10167 F.sub.1 = -0.12656 G.sub.1 = -0.23402 (n.sub.0 - 1)f/r.sub.1 = 0.33 (n.sub.0 - 1)f/r.sub.2 = -0.57 -r.sub.1 /r.sub.2 = 1.75 |n.sub.0 n.sub.2 /4n.sub.1.sup.2 | = 0.31 ______________________________________

Claim 11

A graded refractive index lens according to claim 1, both the refracting surfaces geing aspherical surfaces, wherein said graded refractive index lens has the following numerical data: ______________________________________ f = 1.0 NA = 0.53 IH = 0.0245 WD = 0.441 r.sub.1 = 7.901 d = 1.425 n.sub.0 = 1.65 n.sub.1 = -0.26535 r.sub.2 = -1.529 n.sub.2 = -0.4705 × 10.sup.-1 P.sub.1 = 56.1512 E.sub.1 = -0.2261 F.sub.1 = -0.18002 G.sub.1 = -0.40507 P.sub.2 = -4.2631 E.sub.2 = -0.22154 F.sub.2 = 0.18119 (n.sub.0 - 1)f/r.sub.1 = 0.08 (n.sub.0 - 1)f/r.sub.2 = -0.43 -r.sub.1 /r.sub.2 = 5.17 |n.sub.0 n.sub.2 /4n.sub.1.sup.2 | = 0.27 ______________________________________

Claim 12

A graded refractive index lens in which the refractive index n at the radial distance r from the optical axis is expressed by the formula shown below on the premise that n 0 represents the refractive index on the optical axis of said lens, n 1 , n 2 , . . . respectively represent the 2nd-, 4th-, . . . order coefficients: n=n.sub.0 +n.sub.1 r.sup.2 +n.sub.2 r.sup.4 +. . . and in which the shapes of both an incident side refracting surface and an exit side refracting surface of said lens have positive refracting powers and at least said incident side refracting surface is aspherical and is expressed by Equation (A) shown below, and said graded refractive index lens satisfies the following conditions (4), (5) and (6): ##EQU3## 0.9<(n.sub.0 -1)f/r.sub.1 <1.3 (4)

Claim 13

A graded refractive index lens in which the refractive index n at the radial distance r from the optical axis is expressed by the formula shown below on the premise that n 0 represents the refractive index on the optical axis of said lens, n 1 , n 2 , . . . respectively represent the 2nd-, 4th-, . . . order coefficients: n=n.sub.0 +n.sub.1 r.sup.2 +n.sub.2 r.sup.4 +. . . and in which the shapes of both an incident side refracting surface and an exit side refracting surface of said lens have positive refracting powers and at least said incident side refracting surface is aspherical and is expressed by Equation (A) shown below, and said graded refractive index lens satisfies the following conditions (4), (5) and (6): ##EQU3## 0.9<(n.sub.0 -1)f/r.sub.1 <1.3 (4)

Claim 14

25<-(n 0 -1)f/r 2 <0.7 (5) 0.1<n.sub.1 f.sup.2 <0.4 (6) where C represents the curvature of the vertex portion of said aspherical surface, P represents the constant of cone, E, F, G, . . . respectively represent the 4th-, 6th-, 8th-, . . . order coefficients of r, r 1 represents the radius of curvature of the incident side refracting surface of said lens, r 2 represents the radius of curvature of the exit side refracting surface of said lens and f represents the focal length of said lens.

Claim 15

25<-(n 0 -1)f/r 2 <0.7 (5) 0.1<n.sub.1 f.sup.2 <0.4 (6) where C represents the curvature of the vertex portion of said aspherical surface, P represents the constant of cone, E, F, G, . . . respectively represent the 4th-, 6th-, 8th-, . . . order coefficients of r, r 1 represents the radius of curvature of the incident side refracting surface of said lens, r 2 represents the radius of curvature of the exit side refracting surface of said lens and f represents the focal length of said lens.

Claim 16

A graded refractive index lens according to claim 9, further satisfying the following condition: |n.sub.0 n.sub.2 /4n.sub.1.sup.2 |<1000

Claim 17

A graded refractive index lens according to claim 9, said incident side refracting surface being an aspherical surface, wherein said graded refractive index lens has the following numerical data: ______________________________________ f = 1.0 NA = 0.47 IH = 0.0217 WD = 0.533 r.sub.1 = 0.673 d = 0.652 n.sub.0 = 1.65 n.sub.1 = 0.35074 r.sub.2 = -1.089 n.sub.2 = 1.197 P.sub.1 = 0.7485 E.sub.1 = -0.73361 × 10.sup.-1 F.sub.1 = -1.2325 G.sub.1 = -2.7273 (n.sub.0 - 1)f/r.sub.1 = 0.97 (n.sub.0 - 1)f/r.sub.2 = -0.60 -r.sub.1 /r.sub.2 = 0.62 |n.sub.0 n.sub.2 /4n.sub.1.sup.2 | = 4.01 ______________________________________

Claim 18

A graded refractive index lens according to claim 9, both the refracting surfaces being aspherical surfaces, wherein said graded refractive index lens has the following numerical data: ______________________________________ f = 1.0 NA = 0.47 IH = 0.0217 WD = 0.326 r.sub.1 = 0.629 d = 0.898 n.sub.0 = 1.63891 n.sub.1 = 0.1169 r.sub.2 = -2.256 n.sub.2 = 0.37458 P.sub.1 = 0.5929 E.sub.1 = 0.79635 × 10.sup.-1 F.sub.1 = -0.93793 × 10.sup.-1 P.sub.2 = 11.1960 E.sub.2 = 1.0439 F.sub.2 = 0.22858 (n.sub.0 - 1)f/r.sub.1 = 1.02 (n.sub.0 - 1)f/r.sub.2 = -0.28 -r.sub.1 /r.sub.2 = 0.28 |n.sub.0 n.sub.2 /4n.sub.1.sup.2 | = 11.23 ______________________________________

Claim 19

A graded refractive index lens according to claim 9, both the refracting surfaces being aspherical surfaces, wherein said graded refractive index lens has the following numerical data: ______________________________________ f = 1.0 NA = 0.47 IH = 0.0217 WD = 0.326 r.sub.1 = 0.641 d = 0.903 n.sub.0 = 1.76137 n.sub.1 = 0.26565 r.sub.2 = -2.298 n.sub.2 = 0.46556 P.sub.1 = 0.4856 E.sub.1 = 0.72935 × 10.sup.-1 F.sub.1 = -0.90985 × 10.sup.-1 P.sub.2 = -26.6506 E.sub.2 = 0.68882 F.sub.2 = -0.29421 (n.sub.0 - 1)f/r.sub.1 = 1.19 (n.sub.0 - 1)f/r.sub.2 = -0.33 -r.sub.1 /r.sub.2 = 0.28 |n.sub.0 n.sub.2 /4n.sub.1.sup.2 | = 2.91 ______________________________________

Claim 20

A graded refractive index lens in which the refractive index n at the radial distance r from the optical axis is expressed by the formula shown below on the premise that n 0 represents the refractive index on the optical axis of said lens, n 1 , n 2 , . . . respectively represent the 2nd-, 4th-, . . . order coefficients: n=n.sub.0 +n.sub.1 r.sup.2 +n.sub.2 r.sup.4 +. . . and in which an incident side refracting surface is aspherical and is expressed by Equation (A) shown below, and said graded refractive index lens has the following numerical data: ______________________________________ ##STR1## (A) f = 1.0 NA = 0.47 IH = 0.0217 WD = 0.355 r.sub.1 = 0.824 d = 0.978 n.sub.0 = 1.65 n.sub.1 = -0.25718 × 10.sup.-1 r.sub.2 = -1.955 n.sub.2 = 0.22661 P.sub.1 = -0.0036 E.sub.1 = 0.20545 F.sub.1 = -0.40244 × 10.sup.-1 (n.sub.0 - 1)f/r.sub.1 = 0.79 (n.sub.0 - 1)f/r.sub.2 = -0.33 -r.sub.1 /r.sub.2 = 0.42 |n.sub.0 n.sub.2 /4n.sub.1.sup.2 | = 141.3 G.sub.1 = - 0.18874 ______________________________________ where C represents the curvature of the vertex portion of said aspherical surface, P represents the constant of cone, E, F, G, . . . respectively represent the 4th-, 6th-, 8th-, . . . order coefficients of r, r 1 represents the radius of curvature of the incident side refracting surface of said lens, r 2 represents the radius of curvature of the exit side refracting surface of said lens and f represents the focal length of said lens.

Claim 21

A graded refractive index lens in which the refractive index n at the radial distance r from the optical axis is expressed by the formula shown below on the premise that n 0 represents the refractive index on the optical axis of said lens, n 1 , n 2 , . . . respectively represent the 2nd-, 4th-, . . . order coefficients: n=n.sub.0 +n.sub.1 r.sup.2 +n.sub.2 r.sup.4 +. . . and in which an incident side refracting surface is aspherical and is expressed by Equation (A) shown below, and said graded refractive index lens has the following numerical data: ______________________________________ ##STR1## (A) f = 1.0 NA = 0.47 IH = 0.0217 WD = 0.355 r.sub.1 = 0.824 d = 0.978 n.sub.0 = 1.65 n.sub.1 = -0.25718 × 10.sup.-1 r.sub.2 = -1.955 n.sub.2 = 0.22661 P.sub.1 = -0.0036 E.sub.1 = 0.20545 F.sub.1 = -0.40244 × 10.sup.-1 (n.sub.0 - 1)f/r.sub.1 = 0.79 (n.sub.0 - 1)f/r.sub.2 = -0.33 -r.sub.1 /r.sub.2 = 0.42 |n.sub.0 n.sub.2 /4n.sub.1.sup.2 | = 141.3 G.sub.1 = - 0.18874 ______________________________________ where C represents the curvature of the vertex portion of said aspherical surface, P represents the constant of cone, E, F, G, . . . respectively represent the 4th-, 6th-, 8th-, . . . order coefficients of r, r 1 represents the radius of curvature of the incident side refracting surface of said lens, r 2 represents the radius of curvature of the exit side refracting surface of said lens and f represents the focal length of said lens.

Claim 22

A graded refractive index lens in which the refractive index n at the radial distance r from the optical axis is expressed by the formula shown below on the premise that n 0 represents the refractive index on the optical axis of said lens, n 1 , n 2 , . . . respectively represent the 2nd-, 4th-, . . . order coefficients: n=n.sub.0 n.sub.1 r.sup.2 +n.sub.2 r.sup.4 +. . . and in which both refracting surfaces are aspherical and are expressed by Equation (A) shown below, and said graded refractive index lens has the following numerical data: ______________________________________ ##STR2## (A) f = 1.0 NA = 0.47 IH = 0.0217 WD = 0.303 r.sub.1 = 0.727 d = 1.005 n.sub.0 = 1.50254 n.sub.1 = -0.12421 r.sub.2 = -1.910 n.sub.2 = 0.59222 × 10.sup.-1 P.sub.1 = 0.1849 E.sub.1 = 0.23647 F.sub.1 = 0.15196 G.sub.1 = 0.15752 P.sub.2 = -20.2068 E.sub.2 = 0.25202 F.sub.2 = -0.51597 (n.sub.0 - 1)f/r.sub.1 = 0.69 (n.sub.0 - 1)f/r.sub.2 = -0.26 -r.sub.1 /r.sub.2 = 0.38 |n.sub. 0 n.sub.2 /4n.sub.1.sup.2 | = 1.44 ______________________________________ where C represents the curvature of the vertex portion of said aspherical surface, P represents the constant of cone, E, F, G, . . . respectively represent the 4th-, 6th-, 8th-, . . . order coefficients of r, r 1 represents the radius of curvature of the incident side refracting surface of said lens, r 2 represents the radius of curvature of the exit side refracting surface of said lens and f represents the focal length of said lens.

Claim 23

A graded refractive index lens in which the refractive index n at the radial distance r from the optical axis is expressed by the formula shown below on the premise that n 0 represents the refractive index on the optical axis of said lens, n 1 , n 2 , . . . respectively represent the 2nd-, 4th-, . . . order coefficients: n=n.sub.0 n.sub.1 r.sup.2 +n.sub.2 r.sup.4 +. . . and in which both refracting surfaces are aspherical and are expressed by Equation (A) shown below, and said graded refractive index lens has the following numerical data: ______________________________________ ##STR2## (A) f = 1.0 NA = 0.47 IH = 0.0217 WD = 0.303 r.sub.1 = 0.727 d = 1.005 n.sub.0 = 1.50254 n.sub.1 = -0.12421 r.sub.2 = -1.910 n.sub.2 = 0.59222 × 10.sup.-1 P.sub.1 = 0.1849 E.sub.1 = 0.23647 F.sub.1 = 0.15196 G.sub.1 = 0.15752 P.sub.2 = -20.2068 E.sub.2 = 0.25202 F.sub.2 = -0.51597 (n.sub.0 - 1)f/r.sub.1 = 0.69 (n.sub.0 - 1)f/r.sub.2 = -0.26 -r.sub.1 /r.sub.2 = 0.38 |n.sub. 0 n.sub.2 /4n.sub.1.sup.2 | = 1.44 ______________________________________ where C represents the curvature of the vertex portion of said aspherical surface, P represents the constant of cone, E, F, G, . . . respectively represent the 4th-, 6th-, 8th-, . . . order coefficients of r, r 1 represents the radius of curvature of the incident side refracting surface of said lens, r 2 represents the radius of curvature of the exit side refracting surface of said lens and f represents the focal length of said lens.

Claim 24

A graded refractive index lens in which the refractive index n at the radial distance r from the optical axis is expressed by the formula shown below on the premise that n 0 represents the refractive index on the optical axis of said lens, n 1 , n 2 , . . . respectively represent the 2nd-, 4th-, . . . order coefficients: n=n.sub.0 +n.sub.1 r.sup.2 +n.sub.2 r.sup.4 +. . . and in which both refracting surfaces are aspherical and are expressed by Equation (A) shown below, and said graded refractive index lens has the following numerical data: ______________________________________ ##STR3## (A) f = 1.0 NA = 0.47 IH = 0.0217 WD = 0.326 r.sub.1 = 0.681 d = 0.946 n.sub.0 = 1.5 n.sub.1 = -0.92432 × 10.sup.-1 r.sub.2 = -1.828 n.sub.2 = 0.11014 P.sub.1 = 0.2684 E.sub.1 = 0.24188 F.sub.1 = 0.15376 G.sub.1 = 0.25946 P.sub.2 = -13.3374 E.sub.2 = 0.3981 F.sub.2 = -0.40139 (n.sub.0 - 1)f/r.sub.1 = 0.73 (n.sub.0 - 1)f/r.sub.2 = -0.27 -r.sub.1 /r.sub.2 = 0.37 |n.sub.0 n.sub.2 /4n.sub.1.sup.2 | = 4.83 ______________________________________ where C represents the curvature of the vertex portion of said aspherical surface, P represents the constant of cone, E, F, G, . . . respectively represent the 4th-, 6th-, 8th, . . . order coefficients of r, r 1 represents the radius of curvature of the incident side refracting surface of said lens, r 2 represents the radius of curvature of the exit side refracting surface of said lens and f represents the focal length of said lens.

Claim 25

A graded refractive index lens in which the refractive index n at the radial distance r from the optical axis is expressed by the formula shown below on the premise that n 0 represents the refractive index on the optical axis of said lens, n 1 , n 2 , . . . respectively represent the 2nd-, 4th-, . . . order coefficients: n=n.sub.0 +n.sub.1 r.sup.2 +n.sub.2 r.sup.4 +. . . and in which both refracting surfaces are aspherical and are expressed by Equation (A) shown below, and said graded refractive index lens has the following numerical data: ______________________________________ ##STR3## (A) f = 1.0 NA = 0.47 IH = 0.0217 WD = 0.326 r.sub.1 = 0.681 d = 0.946 n.sub.0 = 1.5 n.sub.1 = -0.92432 × 10.sup.-1 r.sub.2 = -1.828 n.sub.2 = 0.11014 P.sub.1 = 0.2684 E.sub.1 = 0.24188 F.sub.1 = 0.15376 G.sub.1 = 0.25946 P.sub.2 = -13.3374 E.sub.2 = 0.3981 F.sub.2 = -0.40139 (n.sub.0 - 1)f/r.sub.1 = 0.73 (n.sub.0 - 1)f/r.sub.2 = -0.27 -r.sub.1 /r.sub.2 = 0.37 |n.sub.0 n.sub.2 /4n.sub.1.sup.2 | = 4.83 ______________________________________ where C represents the curvature of the vertex portion of said aspherical surface, P represents the constant of cone, E, F, G, . . . respectively represent the 4th-, 6th-, 8th, . . . order coefficients of r, r 1 represents the radius of curvature of the incident side refracting surface of said lens, r 2 represents the radius of curvature of the exit side refracting surface of said lens and f represents the focal length of said lens.