Optical system comprising a single element having a continuously varying index of refraction

Claim 2

A singlet lens having an axial index of refraction gradient according to an equation of the form N(x) N00 + N01x + N02x2 + . . . where N00, N01, and N02 are the coefficients of the first, second and third terms, respectively, of a power series expansion of N(x), the index of refraction of the lens as a function of x, the distance along the optical axis of the lens measured from the vertex of the first surface, said lens having a thickness t, a first curvature CV1, a second curvature CV2, and a focal length F.L., said lens further having at least the third-order spherical aberration and coma thereof simultaneously reduced, the reduction in spherical aberration and coma being effected by selective adjustments to N01, the coefficient of the second term of the index of refraction equation, and to CV1, respectively, and the focal length F.L. being determined by CV2.

Claim 3

An optical system comprising, in combination, a singlet lens and a stop, said lens having an axial index of refraction gradient according to an equation of the form N(x) N00 + N01x + N02x2+ . . . , where N00, N01 and N02 are the coefficients of the first, second and third terms, respectively, of a power series expansion of N(x), the index of refraction of the lens as a function of x, the distance along the optical axis of the lens measured from the vertex of the first surface, said lens having a thickness t, a first curvature CV1, a second curvature CV2, and a focal length F.L. and the lens to stop distance being Ds, said system having at least the third-order spherical aberration, coma and distortion thereof simultaneously reduced, the reduction in spherical aberration, coma and distortion being effected by selective adjustments to N01 the coefficient of the second term of said index of refraction equation, CV1 and Ds, respectively, and the focal length F.L. being determined by CV2.

Claim 4

An optical system comprising, in combination, a singlet lens and a stop, said lens having an axial index of refraction gradient according to an equation of the form N(x) N00 + N01x + N02x2+ . . . , where N00, N01 and N02 are the coefficients of the first, second and third terms, respectively, of a power series expansion of N(x), the index of refraction of the lens as a function of x, the distance along the optical axis of the lens measured from the vertex of the first surface, said lens having a thickness t, a first curvature CV1, a second curvature CV2, and a focal length F.L. and the lens to stop distance being Ds, said system having at least the third-order spherical aberration, coma and distortion thereof simultaneously reduced, the reduction in spherical aberration, coma and distortion being effected by selective adjustments to N01 the coefficient of the second term of said index of refraction equation, CV1 and Ds, respectively, and the focal length F.L. being determined by CV2.

Claim 5

A singlet lens having a radial index of refraction gradient according to an equation of the form N( Rho ) N00 + N10 Rho 2 + N20 Rho 4 + . . . , where, Rho 2 y2 + z2, and N00, N10, and N20 are the coefficients of the first, second and third terms, respectively, of a power series expansion of N( Rho ), the index of refraction of the lens as a function of Rho , Rho 2 y2 + z2, where y and z represent distances measured along the two orthogonal coordinates of the lens, said orthogonal axes intercepting the optical axis of the lens, said lens having a thickness t, a first curvature CV1, a second curvature CV2, and a focal length F.L., said lens further having at least the third-order spherical aberration, coma and astigmatism thereof simultaneously reduced, the reduction in spherical aberration and coma and astigmatism being effected by selective adjustments to: N20, the coefficient of the third term of the index of refraction equation; and t, CV1 and N10, the coefficient of the second term in the index of refraction equation, respectively, and the focal length F.L. being determined by CV2.

Claim 6

A singlet lens having a radial index of refraction gradient according to an equation of the form N( Rho ) N00 + N10 Rho 2 + N20 Rho 4 + . . . , where, Rho 2 y2 + z2, and N00, N10, and N20 are the coefficients of the first, second and third terms, respectively, of a power series expansion of N( Rho ), the index of refraction of the lens as a function of Rho , Rho 2 y2 + z2, where y and z represent distances measured along the two orthogonal coordinates of the lens, said orthogonal axes intercepting the optical axis of the lens, said lens having a thickness t, a first curvature CV1, a second curvature CV2, and a focal length F.L., said lens further having at least the third-order spherical aberration, coma and astigmatism thereof simultaneously reduced, the reduction in spherical aberration and coma and astigmatism being effected by selective adjustments to: N20, the coefficient of the third term of the index of refraction equation; and t, CV1 and N10, the coefficient of the second term in the index of refraction equation, respectively, and the focal length F.L. being determined by CV2.

Claim 7

An optical system comprising, in combination, a singlet lens and a stop, said lens having a radial index of refraction gradient according to an equation of the form N( Rho ) N00 + N10 Rho 2 + N20 Rho 4 + . . . , where, Rho 2 y2 + z2, and N00, N10, and N20 are the coefficients of the first, second and third terms, respectively, of a power series expansion of N( Rho ), the index of refraction of the lens as a function of Rho , Rho 2 y2 + z2, where y and z represent distances measured along the two orthogonal coordinates of the lens, said orthogonal axes intercepting the optical axis of the lens, said lens having a thickness t, a first curvature CV1, a second curvature CV2, and a focal length F.L., and the lens to stop distance being Ds, said lens having at least the third-order spheRical aberration, coma, astigmatism and distortion thereof simultaneously reduced, the reduction in spherical aberration, distortion, and coma and astigmatism, being effected by selective adjustments to: N20, the coefficient of the third term in said index of refraction equation; Ds; and, CV1,t, and N10, the coefficient of the second term of said index of refraction equation, respectively, and the focal length F.L. being determined by CV2.

Claim 8

An optical system comprising, in combination, a singlet lens and a stop, said lens having a radial index of refraction gradient according to an equation of the form N( Rho ) N00 + N10 Rho 2 + N20 Rho 4 + . . . , where, Rho 2 y2 + z2, and N00, N10, and N20 are the coefficients of the first, second and third terms, respectively, of a power series expansion of N( Rho ), the index of refraction of the lens as a function of Rho , Rho 2 y2 + z2, where y and z represent distances measured along the two orthogonal coordinates of the lens, said orthogonal axes intercepting the optical axis of the lens, said lens having a thickness t, a first curvature CV1, a second curvature CV2, and a focal length F.L., and the lens to stop distance being Ds, said lens having at least the third-order spheRical aberration, coma, astigmatism and distortion thereof simultaneously reduced, the reduction in spherical aberration, distortion, and coma and astigmatism, being effected by selective adjustments to: N20, the coefficient of the third term in said index of refraction equation; Ds; and, CV1,t, and N10, the coefficient of the second term of said index of refraction equation, respectively, and the focal length F.L. being determined by CV2.

Claim 9

A singlet lens having plane, parallel surfaces and a radial index of refraction gradient according to an equation of the form N( Rho ) N00 + N10 Rho 2 + N20 Rho 4 + . . . , where, Rho 2 y2 + z2, and N00, N10, and N20 are the coefficients of the first, second and third terms, respectively, of a power series expansion of N( Rho ), the index of refraction of the lens as a function of Rho , Rho 2 y2 + z2, where y and z represent distances measured along the two orthogonal coordinates of the lens, said orthogonal axes intercepting the optical axis of the lens, said lens having a thickness t and and a focal length F.L., said lens further having at least the third-order spherical aberration thereof reduced, said focal length being established by selective variation of N10, the coefficient of the second term of said index of refraction equation, and said reduction in spherical aberration being effected by selective variation of N20, the coefficient of the third term of said index of refraction equation, the product of thickness t and N10 being substantially constant for any given focal length F.L.

Claim 10

A singlet lens having plane, parallel surfaces and a radial index of refraction gradient according to an equation of the form N( Rho ) N00 + N10 Rho 2 + N20 Rho 4 + . . . , where, Rho 2 y2 + z2, and N00, N10, and N20 are the coefficients of the first, second and third terms, respectively, of a power series expansion of N( Rho ), the index of refraction of the lens as a function of Rho , Rho 2 y2 + z2, where y and z represent distances measured along the two orthogonal coordinates of the lens, said orthogonal axes intercepting the optical axis of the lens, said lens having a thickness t and and a focal length F.L., said lens further having at least the third-order spherical aberration thereof reduced, said focal length being established by selective variation of N10, the coefficient of the second term of said index of refraction equation, and said reduction in spherical aberration being effected by selective variation of N20, the coefficient of the third term of said index of refraction equation, the product of thickness t and N10 being substantially constant for any given focal length F.L.

Claim 11

An optical system comprising, in combination, a singlet lens and a stop, said lens having an axial index of refraction gradient according to an equation of the form N(x) N00 + N01x . . . , said lens further having a thickness t, a first curvature CV1 and a second curvature CV2, wherein for a starting value of the index of refraction N00 1.65, a focal length F.L. 10.0 units, and infinite conjugates, the relationship between CV1, CV2, the stop to lens distance Ds, and N01, the coefficient of the second term of the index of refraction equation, as a function of thickness t, is substantially given by the following table, and interpolations and extrapolations thereof, whereby at least the third-order spherical aberration, coma, and distortion of said system are simultaneously reduced N00 1.65 Focal Length 10.0 Infinite Conjugates t N01 CV1 CV2 Ds0.10 -0.060655 +0.157835 +0.004036 +0.015429 0.25 -0.060635 +0.157501 +0.003786 +0.039080 0.50 -0.060608 +0.156937 +0.003330 +0.079900 1.00 -0.060580 +0.155772 +0.002247 +0.167158 1.50 -0.060595 +0.154551 +0.000885 +0.262651

Claim 12

An optical system comprising, in combination, a singlet lens and a stop, said lens having an axial index of refraction gradient according to an equation of the form N(x) N00 + N01x . . . , said lens further having a thickness t, a first curvature CV1 and a second curvature CV2, wherein for a starting value of the index of refraction N00 1.65, a focal length F.L. 10.0 units, and infinite conjugates, the relationship between CV1, CV2, the stop to lens distance Ds, and N01, the coefficient of the second term of the index of refraction equation, as a function of thickness t, is substantially given by the following table, and interpolations and extrapolations thereof, whereby at least the third-order spherical aberration, coma, and distortion of said system are simultaneously reduced N00 1.65 Focal Length 10.0 Infinite Conjugates t N01 CV1 CV2 Ds0.10 -0.060655 +0.157835 +0.004036 +0.015429 0.25 -0.060635 +0.157501 +0.003786 +0.039080 0.50 -0.060608 +0.156937 +0.003330 +0.079900 1.00 -0.060580 +0.155772 +0.002247 +0.167158 1.50 -0.060595 +0.154551 +0.000885 +0.262651

Claim 13

An optical system comprising, in combination, a singlet lens and a stop, said lens having an axial index of refraction gradient according to an equation of the form N(x) N00 + N01x . . . said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a starting value of the index of refraction N00 1.65, a lens thickness t 1.0 units, and infinite conjugates, the relationship between CV1, CV2, the stop to lens distance Ds, and N01, the coefficient of the second term in the index of refraction equation, as a function of the focal length, F.L., is substantially given by the following table, and interpolations and extrapolations thereof, whereby at least the third-order spherical aberration, coma, and distortion of said system are simultaneously reduced N00 1.65 Thickness 1.0 Infinite Conjugates F.L. N01 CV1 CV2 Ds-20 +0.030849 -0.079485 -0.002386 +0.146020 -10 +0.060822 -0.160173 -0.005461 +0.140520 -05 +0.122204 -0.324328 -0.012478 +0.129779 5 -0.121316 +0.306526 -0.001662 +0.183669 10 -0.060580 +0.155772 +0.002247 +0.167158 13.3 -0.045447 +0.117271 +0.002110 +0.163439 15.0 -0.040403 +0.104369 +0.001991 +0.162280 20.0 -0.030314 +0.078468 +0.001656 +0.159820

Claim 14

An optical system comprising, in combination, a singlet lens and a stop, said lens having an axial index of refraction gradient according to an equation of the form N(x) N00 + N01x . . . said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a starting value of the index of refraction N00 1.65, a lens thickness t 1.0 units, and infinite conjugates, the relationship between CV1, CV2, the stop to lens distance Ds, and N01, the coefficient of the second term in the index of refraction equation, as a function of the focal length, F.L., is substantially given by the following table, and interpolations and extrapolations thereof, whereby at least the third-order spherical aberration, coma, and distortion of said system are simultaneously reduced N00 1.65 Thickness 1.0 Infinite Conjugates F.L. N01 CV1 CV2 Ds-20 +0.030849 -0.079485 -0.002386 +0.146020 -10 +0.060822 -0.160173 -0.005461 +0.140520 -05 +0.122204 -0.324328 -0.012478 +0.129779 5 -0.121316 +0.306526 -0.001662 +0.183669 10 -0.060580 +0.155772 +0.002247 +0.167158 13.3 -0.045447 +0.117271 +0.002110 +0.163439 15.0 -0.040403 +0.104369 +0.001991 +0.162280 20.0 -0.030314 +0.078468 +0.001656 +0.159820

Claim 15

An optical system comprising, in combination, a singlet lens and a stop, said lens having an axial index of refraction gradient according to an equation of the form N(x) N00 + N01x . . . said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a lens thickness t 1.0 units, a focal length, F.L. 10.0 units, and infinite conjugates, the relationship between CV1, CV2, the stop to lens distance Ds, and N01, the coefficient of the second term of the index of refraction equation, as a function of N00, the starting value of the index of refraction, is substantially given by the following table, and interpolations and extrapolations thereof, whereby at least the third-order spherical aberration, coma, and distortion of said system are simultaneously reduced Thickness 1.0 Focal Length 10.0 Infinite Conjugates N00 N01 CV1CV2 Ds 1.50 -0.069525 +0.176928 -0.029158 +0.256973 1.65 -0.060580 +0.155772 +0.002247 +0.167158 1.70 -0.058830 +0.150876 +0.009328 +0.136956 1.80 -0.056227 +0.142977 +0.020656 +0.075885

Claim 16

An optical system comprising, in combination, a singlet lens and a stop, said lens having an axial index of refraction gradient according to an equation of the form N(x) N00 + N01x . . . said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a lens thickness t 1.0 units, a focal length, F.L. 10.0 units, and infinite conjugates, the relationship between CV1, CV2, the stop to lens distance Ds, and N01, the coefficient of the second term of the index of refraction equation, as a function of N00, the starting value of the index of refraction, is substantially given by the following table, and interpolations and extrapolations thereof, whereby at least the third-order spherical aberration, coma, and distortion of said system are simultaneously reduced Thickness 1.0 Focal Length 10.0 Infinite Conjugates N00 N01 CV1CV2 Ds 1.50 -0.069525 +0.176928 -0.029158 +0.256973 1.65 -0.060580 +0.155772 +0.002247 +0.167158 1.70 -0.058830 +0.150876 +0.009328 +0.136956 1.80 -0.056227 +0.142977 +0.020656 +0.075885

Claim 17

An optical system comprising, in combination, a singlet lens and a stop, said lens having an axial index of refraction gradient according to an equation of the form N(x) N00 + N01x . . . said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a focal length F.L. 10.0 units, a thickness t 1.0 units, and a starting value of the index of refraction N00 1.65, the relationship between CV1, CV2, the stop to lens distance Ds, and N01, the coefficient of the second term of the index of refraction equation, as a function of the objecT-image conjugates, is substantially given by the following table, and interpolations and extrapolations thereof, whereby at least the third-order spherical aberration, coma, and distortion of said system are simultaneously reduced N00 1.65 Focal Length 10.0 Thickness 1.0 Conjugates N01 CV1 CV2 Ds Infinity -0.060580 +0.155772 +0.002247 +0.167158 20:1 -0.068290 +0.148095 -0.006926 +0.201966 10:1 -0.077089 +0.141083 -0.015431 +0.233494 5:1 -0.099553 +0.128723 -0.031091 +0.288665 2:1 -0.216947 +0.108385 -0.069923 +0.380051

Claim 18

An optical system comprising, in combination, a singlet lens and a stop, said lens having an axial index of refraction gradient according to an equation of the form N(x) N00 + N01x . . . said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a focal length F.L. 10.0 units, a thickness t 1.0 units, and a starting value of the index of refraction N00 1.65, the relationship between CV1, CV2, the stop to lens distance Ds, and N01, the coefficient of the second term of the index of refraction equation, as a function of the objecT-image conjugates, is substantially given by the following table, and interpolations and extrapolations thereof, whereby at least the third-order spherical aberration, coma, and distortion of said system are simultaneously reduced N00 1.65 Focal Length 10.0 Thickness 1.0 Conjugates N01 CV1 CV2 Ds Infinity -0.060580 +0.155772 +0.002247 +0.167158 20:1 -0.068290 +0.148095 -0.006926 +0.201966 10:1 -0.077089 +0.141083 -0.015431 +0.233494 5:1 -0.099553 +0.128723 -0.031091 +0.288665 2:1 -0.216947 +0.108385 -0.069923 +0.380051

Claim 19

An optical system comprising, in combination, a singlet lens and a stop, said lens having a zone therein having an axial index of refraction gradient according to an equation of the form N(x) N00 + N01x . . . said zone being bounded by a plane which is parallel to the x-z plane of the system, said lens further having a thickness t, a first curvature CV1, and a second curvature, CV2, wherein for a starting value of the index of refraction N00 1.65, a lens thickness of t 1.0 units, a focal length of F.L. 10.0 units, and infinite conjugates, the relationship between CV1, CV2, the lens to stop distance Ds, and N01, the coefficient of the second term in the index of refraction equation, as a function of P, the position, in units, of the zone boundary plane from the front surface of the lens, is substantially given by the following table, and interpolations and extrapolations thereof, whereby at least the third-order spherical aberration, coma, and distortion of said system are simultaneously reduced N00 1.65 F.L. 10.0 Thickness 1.0 Infinite Conjugates P N01 CV1CV2 Ds0.5 +0.060708 -0.160172 -0.005703 +0.139722 0.2 +0.060715 -0.160132 -0.005821 +0.139721 0.1 +0.060719 -0.160115 -0.005858 +0.03469 0.05 +0.060721 -0.160106 -0.005875 +0.089514 0.01 +0.060723 -0.160098 -0.005890 +0.129413

Claim 20

An optical system comprising, in combination, a singlet lens and a stop, said lens having a zone therein having an axial index of refraction gradient according to an equation of the form N(x) N00 + N01x . . . said zone being bounded by a plane which is parallel to the x-z plane of the system, said lens further having a thickness t, a first curvature CV1, and a second curvature, CV2, wherein for a starting value of the index of refraction N00 1.65, a lens thickness of t 1.0 units, a focal length of F.L. 10.0 units, and infinite conjugates, the relationship between CV1, CV2, the lens to stop distance Ds, and N01, the coefficient of the second term in the index of refraction equation, as a function of P, the position, in units, of the zone boundary plane from the front surface of the lens, is substantially given by the following table, and interpolations and extrapolations thereof, whereby at least the third-order spherical aberration, coma, and distortion of said system are simultaneously reduced N00 1.65 F.L. 10.0 Thickness 1.0 Infinite Conjugates P N01 CV1CV2 Ds0.5 +0.060708 -0.160172 -0.005703 +0.139722 0.2 +0.060715 -0.160132 -0.005821 +0.139721 0.1 +0.060719 -0.160115 -0.005858 +0.03469 0.05 +0.060721 -0.160106 -0.005875 +0.089514 0.01 +0.060723 -0.160098 -0.005890 +0.129413

Claim 21

A singlet lens, said lens having an axial index of refraction gradient according to an equation of the form N(x) N00 + N01x . . . said lens further having a thickness t, a first curvature CV1 and a second curvature CV2, wherein for a starting value of the index of refraction N00 1.65, a focal length, F.L. 10.0 units, and infinite conjugates, the relationship between CV1, CV2, and N01, the coefficient of the second term of the index of refraction equation, as a function of the thickness t, is substantially given by the following table, and interpolations and extrapolations thereof, whereby at least the third-order spherical aberration and coma of said lens are simultaneously reduced N00 1.65 Focal Length 10.0 Infinite Conjugates t N01 CV1 CV20.10 -0.060655 +0.157835 +0.004036 0.25 -0.060635 +0.157501 +0.003786 0.50 -0.060608 +0.156937 +0.003330 1.00 -0.060580 +0.155772 +0.002247 1.50 -0.060595 +0.154551 +0.000885

Claim 22

A singlet lens, said lens having an axial index of refraction gradient according to an equation of the form N(x) N00 + N01x . . . said lens further having a thickness t, a first curvature CV1 and a second curvature CV2, wherein for a starting value of the index of refraction N00 1.65, a focal length, F.L. 10.0 units, and infinite conjugates, the relationship between CV1, CV2, and N01, the coefficient of the second term of the index of refraction equation, as a function of the thickness t, is substantially given by the following table, and interpolations and extrapolations thereof, whereby at least the third-order spherical aberration and coma of said lens are simultaneously reduced N00 1.65 Focal Length 10.0 Infinite Conjugates t N01 CV1 CV20.10 -0.060655 +0.157835 +0.004036 0.25 -0.060635 +0.157501 +0.003786 0.50 -0.060608 +0.156937 +0.003330 1.00 -0.060580 +0.155772 +0.002247 1.50 -0.060595 +0.154551 +0.000885

Claim 23

A singlet lens, said lens having an axial index of refraction gradient according to an equation of the form N(x) N00 + N01x . . . said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a starting value of the index of refraction N00 1.65, a lens thickness t 1.0 units, and infinite conjugates, the relationship between CV1, CV2, and N01, the coefficient of the second term in the index of refraction equation, as a function of the focal length, F.L., is substantially given by the following table, and interpolations and extrapolations thereof, whereby at least the third-order spherical aberration and coma of said lens are simultaneously reduced N 1.65 Thickness 1.0 Infinite Conjugates F.L. N01 CV1 CV2-20 +0.030849 -0.079485 -0.002386 -10 +0.060822 -0.160173 -0.005461 -05 +0.122204 -0.324328 -0.012478 +05 -0.121316 +0.306526 -0.001662 +10 -0.060580 +0.155772 +0.002247 +13.3 -0.045447 +0.117271 +0.002110 +15.0 -0.040403 +0.104369 +0.001991 +20.0 -0.030314 +0.078468 +0.001656

Claim 24

A singlet lens, said lens having an axial index of refraction gradient according to an equation of the form N(x) N00 + N01x . . . said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a starting value of the index of refraction N00 1.65, a lens thickness t 1.0 units, and infinite conjugates, the relationship between CV1, CV2, and N01, the coefficient of the second term in the index of refraction equation, as a function of the focal length, F.L., is substantially given by the following table, and interpolations and extrapolations thereof, whereby at least the third-order spherical aberration and coma of said lens are simultaneously reduced N 1.65 Thickness 1.0 Infinite Conjugates F.L. N01 CV1 CV2-20 +0.030849 -0.079485 -0.002386 -10 +0.060822 -0.160173 -0.005461 -05 +0.122204 -0.324328 -0.012478 +05 -0.121316 +0.306526 -0.001662 +10 -0.060580 +0.155772 +0.002247 +13.3 -0.045447 +0.117271 +0.002110 +15.0 -0.040403 +0.104369 +0.001991 +20.0 -0.030314 +0.078468 +0.001656

Claim 25

A singlet lens, said lens having an axial index of refraction gradient according to an equation of the form N(x) N00 + N01x . . . said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a lens thickness t 1.0 units, a focal length F.L. 10.0 units, and infinite conjugates, the relationship between CV1, CV2, and N01, the coefficient of the second term of the index of refraction equation, as a function of N00, the starting value of the index of refraction, is substantially given by the following table, and interpolations and extrapolations thereof, whereby at least the third-order spherical aberration and coma of said lens are simultaneously reduced Thickness 1.0 Focal Length 10.0 Infinite Conjugates N00 N01CV1 CV2+1.50 -0.069525 +0.176928 -0.029158 +1.65 -0.060580 +0.155772 +0.002247 +1.70 -0.058830 +0.150876 +0.009328 +1.80 -0.056227 +0.142977 +0.020656

Claim 26

A singlet lens, said lens having an axial index of refraction gradient according to an equation of the form N(x) N00 + N01x . . . said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a lens thickness t 1.0 units, a focal length F.L. 10.0 units, and infinite conjugates, the relationship between CV1, CV2, and N01, the coefficient of the second term of the index of refraction equation, as a function of N00, the starting value of the index of refraction, is substantially given by the following table, and interpolations and extrapolations thereof, whereby at least the third-order spherical aberration and coma of said lens are simultaneously reduced Thickness 1.0 Focal Length 10.0 Infinite Conjugates N00 N01CV1 CV2+1.50 -0.069525 +0.176928 -0.029158 +1.65 -0.060580 +0.155772 +0.002247 +1.70 -0.058830 +0.150876 +0.009328 +1.80 -0.056227 +0.142977 +0.020656

Claim 27

A singlet lens having an axial index of refraction gradient according to an equation of the form N(x) N00 + N01x . . . said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a focal length, F.L. 10.0 units, a thickness t 1.0 units, and a starting value of the index of refraction N00 1.65, the relationship between CV1, CV2, and N01, the coefficient of the second term oF the index of refraction equation, as a function of the object-image conjugates, is substantially given by the following table, and interpolations and extrapolations thereof, whereby at least the third-order spherical aberration and coma of said lens are simultaneously reduced N 1.65 Focal Length 10.0 Thickness 1.0 Conjugates N01 CV1 CV2 Infinity -0.060580 +0.155772 +0.002247 20:1 -0.068290 +0.148095 -0.006926 10:1 -0.077089 +0.141083 -0.015431 5:1 -0.099553 +0.128723 -0.031091 2:1 -0.216947 +0.108385 -0.069923 1:1

Claim 28

A singlet lens having an axial index of refraction gradient according to an equation of the form N(x) N00 + N01x . . . said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a focal length, F.L. 10.0 units, a thickness t 1.0 units, and a starting value of the index of refraction N00 1.65, the relationship between CV1, CV2, and N01, the coefficient of the second term oF the index of refraction equation, as a function of the object-image conjugates, is substantially given by the following table, and interpolations and extrapolations thereof, whereby at least the third-order spherical aberration and coma of said lens are simultaneously reduced N 1.65 Focal Length 10.0 Thickness 1.0 Conjugates N01 CV1 CV2 Infinity -0.060580 +0.155772 +0.002247 20:1 -0.068290 +0.148095 -0.006926 10:1 -0.077089 +0.141083 -0.015431 5:1 -0.099553 +0.128723 -0.031091 2:1 -0.216947 +0.108385 -0.069923 1:1

Claim 29

A singlet lens having a zone therein having an axial index of refraction gradient according to an equation of the form N(x) N00 + N01x . . . said zone being bounded by a plane which is parallel to the y-z plane of the lens, said lens further having a thickness t, a first curvature CV1, and a second curvature CV1, wherein for a starting value of the index of refraction N00 1.65, a lens thickness of t 1.0 units, a focal length of F.L. 10.0 units, and infinite conjugates, the relationship between CV1, CV2, and N01, the coefficient of the second term in the index of refraction equation, as a function of P, the position, in units, of the zone boundary plane from the front surface of the lens, is substantially given by the following table, and interpolations and extrapolations thereof whereby at least the third-order spherical aberration and coma of said lens are simultaneously reduced N 1.65 F.L. 10.0 Thickness 1.0 Infinite Conjugates P N01CV1 CV2+0.5 +0.060708 -0.160172 -0.005703 +0.2 +0.060715 -0.160132 -0.005821 +0.1 +0.060719 -0.160115 -0.005858 +0.05 +0.060721 -0.160106 -0.005875 +0.01 +0.060723 -0.160098 -0.005890

Claim 30

A singlet lens having a zone therein having an axial index of refraction gradient according to an equation of the form N(x) N00 + N01x . . . said zone being bounded by a plane which is parallel to the y-z plane of the lens, said lens further having a thickness t, a first curvature CV1, and a second curvature CV1, wherein for a starting value of the index of refraction N00 1.65, a lens thickness of t 1.0 units, a focal length of F.L. 10.0 units, and infinite conjugates, the relationship between CV1, CV2, and N01, the coefficient of the second term in the index of refraction equation, as a function of P, the position, in units, of the zone boundary plane from the front surface of the lens, is substantially given by the following table, and interpolations and extrapolations thereof whereby at least the third-order spherical aberration and coma of said lens are simultaneously reduced N 1.65 F.L. 10.0 Thickness 1.0 Infinite Conjugates P N01CV1 CV2+0.5 +0.060708 -0.160172 -0.005703 +0.2 +0.060715 -0.160132 -0.005821 +0.1 +0.060719 -0.160115 -0.005858 +0.05 +0.060721 -0.160106 -0.005875 +0.01 +0.060723 -0.160098 -0.005890

Claim 31

An optical system comprising, in combination, a singlet lens and a stop, said lens having a radial index of refraction gradient according to an equation of the form N( Rho ) N00 + N10 Rho + N20 Rho 2 . . . where, Rho y2 + z2 said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a thickness t 1.75 units, a focal length, F.L. 10 units, and infinite conjugates, the relationship between CV1, CV2, the stop to lens distance Ds, and N10 and N20, the coefficients of the second and third terms of the index of refraction equation, respectively, as a function of the starting value for the index of refraction N00, is substantially given by the following table, and whereby at least the third-order spherical aberration, coma, astigmatism and distortion of said system are simultaneously reduced Thickness 1.75 Focal Length 10.0 Infinite Conjugates N00 N10 N20 CV1 CV2 Ds1.4 +0.06689 +0.023177 +0.255839 -0.561284 +1.050289 1.522 +0.098271 +0.32214 +0.299565 -0.527441 1.6 +0.126280 +0.042136 +0.374174 -0.50294 +0.203626

Claim 32

An optical system comprising, in combination, a singlet lens and a stop, said lens having a radial index of refraction gradient according to an equation of the form N( Rho ) N00 + N10 Rho + N20 Rho 2 . . . where, Rho y2 + z2 said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a thickness t 1.75 units, a focal length, F.L. 10 units, and infinite conjugates, the relationship between CV1, CV2, the stop to lens distance Ds, and N10 and N20, the coefficients of the second and third terms of the index of refraction equation, respectively, as a function of the starting value for the index of refraction N00, is substantially given by the following table, and whereby at least the third-order spherical aberration, coma, astigmatism and distortion of said system are simultaneously reduced Thickness 1.75 Focal Length 10.0 Infinite Conjugates N00 N10 N20 CV1 CV2 Ds1.4 +0.06689 +0.023177 +0.255839 -0.561284 +1.050289 1.522 +0.098271 +0.32214 +0.299565 -0.527441 1.6 +0.126280 +0.042136 +0.374174 -0.50294 +0.203626

Claim 33

An optical system comprising, in combination, a singlet lens and a stop, said lens having a radial index of refraction gradient according to an equation of the form N( Rho ) N00 + N10 Rho + N20 Rho 2 . . . , where, Rho y2 + z2 said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a thickness t 1.75 units, a starting value for the index of refraction N00 1.60 and infinite conjugates, the relationship between CV1, CV2, the stop to lens distance Ds, and N10 and N20, the coefficients of the second and third terms of the index of refraction index, respectively, as a function of the focal length F.L., is substantially given by the following table, and whereby at least the third-order spherical aberration, coma, astigmatism and distortion of said system are simultaneously reduced Thickness 1.75 N00 1.60 Infinite Conjugates F.L. N10N20CV1CV2Ds20 +0.108187 +0.026284 +0.307478 -0.386190 +0.167624 15 +0.114673 +0.031391 +0.321045 -0.435438 +0.182362 10 +0.126280 +0.042136 +0.374174 -0.502954 +0.203626 5 +0.131524 +0.062811 +0.442996 -0.641479 +1.9924

Claim 34

An optical system comprising, in combination, a singlet lens and a stop, said lens having a radial index of refraction gradient according to an equation of the form N( Rho ) N00 + N10 Rho + N20 Rho 2 . . . , where, Rho y2 + z2 said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a thickness t 1.75 units, a starting value for the index of refraction N00 1.60 and infinite conjugates, the relationship between CV1, CV2, the stop to lens distance Ds, and N10 and N20, the coefficients of the second and third terms of the index of refraction index, respectively, as a function of the focal length F.L., is substantially given by the following table, and whereby at least the third-order spherical aberration, coma, astigmatism and distortion of said system are simultaneously reduced Thickness 1.75 N00 1.60 Infinite Conjugates F.L. N10N20CV1CV2Ds20 +0.108187 +0.026284 +0.307478 -0.386190 +0.167624 15 +0.114673 +0.031391 +0.321045 -0.435438 +0.182362 10 +0.126280 +0.042136 +0.374174 -0.502954 +0.203626 5 +0.131524 +0.062811 +0.442996 -0.641479 +1.9924

Claim 35

An optical system comprising, in combination, a singlet lens and a stop, said lens having a radial index of refraction gradient according to an equation of the form N( Rho ) N00 + N10 Rho + N20 Rho 2 . . . , where, Rho y2 + z2 said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a thickness t 1.75 units, a focal length F.L. 10.0 units, a starting value for the index of refraction N00 1.60, the relationship between CV1, CV2, the stop to lens distance Ds, and N10 and N20, the coefficients of the second and third terms of the index of refraction equation, respectively, as a function of the object-image conjugates, is substantially given by the following table, and whereby at least the third-order spherical aberration, coma, astigmatism and distortion of said system are simultaneously reduced Thickness 1.75 Focal Length 10 N00 1.60 Conjugates N10N20CV1CV2Ds Infinity 0.126280 0.042136 0.374174 -0.502954 0.203626 20:1 0.120395 0.039118 0.327927 -0.513103 0.522978 10:1 0.117710 0.037884 0.304176 -0.519038 0.702876 5:1 0.114577 0.036563 0.273485 -0.527172 0.955217 2:1 0.110197 0.035040 0.221524 -0.542673 1.461615 1:1 0.107477 0.034451 0.178295 -0.557495

Claim 36

An optical system comprising, in combination, a singlet lens and a stop, said lens having a radial index of refraction gradient according to an equation of the form N( Rho ) N00 + N10 Rho + N20 Rho 2 . . . , where, Rho y2 + z2 said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a thickness t 1.75 units, a focal length F.L. 10.0 units, a starting value for the index of refraction N00 1.60, the relationship between CV1, CV2, the stop to lens distance Ds, and N10 and N20, the coefficients of the second and third terms of the index of refraction equation, respectively, as a function of the object-image conjugates, is substantially given by the following table, and whereby at least the third-order spherical aberration, coma, astigmatism and distortion of said system are simultaneously reduced Thickness 1.75 Focal Length 10 N00 1.60 Conjugates N10N20CV1CV2Ds Infinity 0.126280 0.042136 0.374174 -0.502954 0.203626 20:1 0.120395 0.039118 0.327927 -0.513103 0.522978 10:1 0.117710 0.037884 0.304176 -0.519038 0.702876 5:1 0.114577 0.036563 0.273485 -0.527172 0.955217 2:1 0.110197 0.035040 0.221524 -0.542673 1.461615 1:1 0.107477 0.034451 0.178295 -0.557495

Claim 37

An optical system comprising, in combination, a singlet lens and a stop, said lens having a radial index of refraction gradient according to an equation of the form N( Rho ) N00 + N10 Rho + N20 Rho 2 . . . , where, Rho y2 + z2 said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a focal length, F.L. 10.0 units, a starting value for the index of refraction N00 1.60 and infinite conjugates, the relationship between CV1, CV2, the stop to lens distance Ds, and N10 and N20, the coefficients of the second and third terms of the index of refraction equation, respectively, as a function of the lens thickness t, is substantially given by the following table, and whereby at least the third-order spherical aberration, coma, astigmatism and distortion of said system are simultaneously reduced Focal Length 10 Infinite Conjugates N00 1.60 Thickness N10 N20CV1CV2Ds3.0 0.045232 0.006746 0.252046 -0.354604 3.423346 2.5 0.061631 0.011826 0.252132 -0.409335 3.890436 2.0 0.090124 0.023948 0.251569 -0.488262 2.380245 1.75 0.126280 0.042136 0.374174 -0.502954 0.203626

Claim 38

An optical system comprising, in combination, a singlet lens and a stop, said lens having a radial index of refraction gradient according to an equation of the form N( Rho ) N00 + N10 Rho + N20 Rho 2 . . . , where, Rho y2 + z2 said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a focal length, F.L. 10.0 units, a starting value for the index of refraction N00 1.60 and infinite conjugates, the relationship between CV1, CV2, the stop to lens distance Ds, and N10 and N20, the coefficients of the second and third terms of the index of refraction equation, respectively, as a function of the lens thickness t, is substantially given by the following table, and whereby at least the third-order spherical aberration, coma, astigmatism and distortion of said system are simultaneously reduced Focal Length 10 Infinite Conjugates N00 1.60 Thickness N10 N20CV1CV2Ds3.0 0.045232 0.006746 0.252046 -0.354604 3.423346 2.5 0.061631 0.011826 0.252132 -0.409335 3.890436 2.0 0.090124 0.023948 0.251569 -0.488262 2.380245 1.75 0.126280 0.042136 0.374174 -0.502954 0.203626

Claim 39

A singlet lens, said lens having a radial index of refraction gradient according to an equation of the form N( Rho ) N00 + N10 Rho + N20 Rho 2 . . . , where, Rho y2 + z2 said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a thickness t 1.75 units, a focal length F.L. 10 units and infinite conjugates, the relationship between CV1, CV2, and N10 and N20, the coefficients of the second and third terms of the index of refraction equation, respectively, as a function of the starting value for the index of refraction N00, is substantially given by the following table, and whereby at least the third-order spherical aberration, coma, and astigmatism of said lens are simultaneously reduced Thickness 1.75 Focal Length 10.0 Infinite Conjugates N00 N10 N20CV1 CV21.4 +0.06689 +0.023177 +0.255839 -0.561284 1.522 +0.098271 +0.32214 +0.299565 -0.527441 1.6 +0.126280 0.042136 +0.374174 -0.50294

Claim 40

A singlet lens, said lens having a radial index of refraction gradient according to an equation of the form N( Rho ) N00 + N10 Rho + N20 Rho 2 . . . , where, Rho y2 + z2 said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a thickness t 1.75 units, a focal length F.L. 10 units and infinite conjugates, the relationship between CV1, CV2, and N10 and N20, the coefficients of the second and third terms of the index of refraction equation, respectively, as a function of the starting value for the index of refraction N00, is substantially given by the following table, and whereby at least the third-order spherical aberration, coma, and astigmatism of said lens are simultaneously reduced Thickness 1.75 Focal Length 10.0 Infinite Conjugates N00 N10 N20CV1 CV21.4 +0.06689 +0.023177 +0.255839 -0.561284 1.522 +0.098271 +0.32214 +0.299565 -0.527441 1.6 +0.126280 0.042136 +0.374174 -0.50294

Claim 41

A singlet lens, said lens having a radial index of refraction gradient according to an equation of the form N( Rho ) N00 + N10 Rho + N20 Rho 2 . . . , where Rho y2 + z2 said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a thickness t 1.75 units, a focal length, F.L. 10 units and infinite conjugates, the relationship between CV1, CV2, and N10 and N20, the coefficients of the second and third terms of the index of refraction equation, respectively, as a function of the starting value for the index of refraction N00, is substantially given by the following table, and whereby at least the third-order spherical aberration, coma, and astigmatism of said lens are simultaneously reduced Thickness 1.75 Focal Length 10.0 Infinite Conjugates N00 N10 N20CV1 CV21.4 -0.084520 +0.002668 +0.209143 +0.853189 1.5 -0.088781 +0.001322 +0.237134 +0.835703 1.6 -0.092238 +0.000117 +0.260641 +0.833375

Claim 42

A singlet lens, said lens having a radial index of refraction gradient according to an equation of the form N( Rho ) N00 + N10 Rho + N20 Rho 2 . . . , where Rho y2 + z2 said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a thickness t 1.75 units, a focal length, F.L. 10 units and infinite conjugates, the relationship between CV1, CV2, and N10 and N20, the coefficients of the second and third terms of the index of refraction equation, respectively, as a function of the starting value for the index of refraction N00, is substantially given by the following table, and whereby at least the third-order spherical aberration, coma, and astigmatism of said lens are simultaneously reduced Thickness 1.75 Focal Length 10.0 Infinite Conjugates N00 N10 N20CV1 CV21.4 -0.084520 +0.002668 +0.209143 +0.853189 1.5 -0.088781 +0.001322 +0.237134 +0.835703 1.6 -0.092238 +0.000117 +0.260641 +0.833375

Claim 43

A singlet lens, said lens having a radial index of refraction gradient according to an equation of the form N( Rho ) N00 + N10 Rho + N20 Rho 2 . . . , where, Rho y2 + z2 said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a thickness t 1.75 units, a starting value for the index of refraction N00 1.60 and infinite conjugates, the relationship between CV1, CV2, and N10 and N20, the coefficients of the second and third terms of the index of refraction index, respectively, as a function of the focal length, F.L., is substantially given by the following table, and whereby at least the third-order spherical aberration, coma, and astigmatism of said lens are simultaneously reduced Thickness 1.75 N00 1.60 Infinite Conjugates F.L. N10 N20CV1 CV220 +0.108187 +0.026284 +0.307478 -0.386190 15 +0.114673 +0.031391 +0.321045 -0.435438 10 +0.126280 +0.042136 +0.374174 -0.502954 5 +0.131524 +0.062811 +0.442996 -0.641479

Claim 44

A singlet lens, said lens having a radial index of refraction gradient according to an equation of the form N( Rho ) N00 + N10 Rho + N20 Rho 2 . . . , where, Rho y2 + z2 said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a thickness t 1.75 units, a starting value for the index of refraction N00 1.60 and infinite conjugates, the relationship between CV1, CV2, and N10 and N20, the coefficients of the second and third terms of the index of refraction index, respectively, as a function of the focal length, F.L., is substantially given by the following table, and whereby at least the third-order spherical aberration, coma, and astigmatism of said lens are simultaneously reduced Thickness 1.75 N00 1.60 Infinite Conjugates F.L. N10 N20CV1 CV220 +0.108187 +0.026284 +0.307478 -0.386190 15 +0.114673 +0.031391 +0.321045 -0.435438 10 +0.126280 +0.042136 +0.374174 -0.502954 5 +0.131524 +0.062811 +0.442996 -0.641479

Claim 45

A singlet lens, said lens having a radial index of refraction gradient according to an equation of the form N( Rho ) N00 + N10 Rho + N20 Rho 2 . . . , where, Rho y2 + z2 said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a thickness t 1.75 units, a starting value for the index of refraction N00 1.60 and infinite conjugates, the relationship between CV1, CV2, and N10 and N20, the coefficients of the second and third terms of the index of refraction index, respectively, as a function of the focal length, F.L., is substantially given by the following table, and whereby at least the third-order spherical aberration, coma, and astigmatism of said lens are simultaneously reduced Thickness 1.75 N00 1.60 Infinite Conjugates F.L. N10 N20CV1 CV2+20 -0.053598 +0.000826 +0.184690 +0.492021 +15 -0.067289 +0.000839 +0.211435 +0.606620 +10 -0.092238 +0.000117 +0.260641 +0.833375 +05 -0.158702 -0.008915 +0.396015 +1.642075

Claim 46

A singlet lens, said lens having a radial index of refraction gradient according to an equation of the form N( Rho ) N00 + N10 Rho + N20 Rho 2 . . . , where, Rho y2 + z2 said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a thickness t 1.75 units, a starting value for the index of refraction N00 1.60 and infinite conjugates, the relationship between CV1, CV2, and N10 and N20, the coefficients of the second and third terms of the index of refraction index, respectively, as a function of the focal length, F.L., is substantially given by the following table, and whereby at least the third-order spherical aberration, coma, and astigmatism of said lens are simultaneously reduced Thickness 1.75 N00 1.60 Infinite Conjugates F.L. N10 N20CV1 CV2+20 -0.053598 +0.000826 +0.184690 +0.492021 +15 -0.067289 +0.000839 +0.211435 +0.606620 +10 -0.092238 +0.000117 +0.260641 +0.833375 +05 -0.158702 -0.008915 +0.396015 +1.642075

Claim 47

A singlet lens, said lens having a radial index of refraction gradient according to an equation of the form N( Rho ) N00 + N10 Rho + N20 Rho 2 . . . , where, Rho y2 + z2 said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a thickness t 1.75 units, a focal length F.L. 10.0 units, a starting value for tHe index of refraction N00 1.60, the relationship between CV1, CV2, and N10 and N20, the coefficients of the second and third terms of the index of refraction equation, respectively, as a function of the object-image conjugates, is substantially given by the following table, and whereby at least the third-order spherical aberration, coma, and astigmatism of said lens are simultaneously reduced Thickness 1.75 Focal Length 10 N00 1.60 Conjugates N10 N20CV1 CV2 Infinity 0.126280 +0.042136 +0.374174 -0.502954 20:1 0.120395 +0.039118 +0.327927 -0.513103 10:1 0.117710 +0.37884 +0.304176 -0.519038 5:1 0.114577 +0.036563 +0.273485 -0.527172 2:1 0.110197 +0.035040 +0.221524 -0.542673 1:1 0.107477 +0.034451 +0.178295 -0.557495

Claim 48

A singlet lens, said lens having a radial index of refraction gradient according to an equation of the form N( Rho ) N00 + N10 Rho + N20 Rho 2 . . . , where, Rho y2 + z2 said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a thickness t 1.75 units, a focal length F.L. 10.0 units, a starting value for tHe index of refraction N00 1.60, the relationship between CV1, CV2, and N10 and N20, the coefficients of the second and third terms of the index of refraction equation, respectively, as a function of the object-image conjugates, is substantially given by the following table, and whereby at least the third-order spherical aberration, coma, and astigmatism of said lens are simultaneously reduced Thickness 1.75 Focal Length 10 N00 1.60 Conjugates N10 N20CV1 CV2 Infinity 0.126280 +0.042136 +0.374174 -0.502954 20:1 0.120395 +0.039118 +0.327927 -0.513103 10:1 0.117710 +0.37884 +0.304176 -0.519038 5:1 0.114577 +0.036563 +0.273485 -0.527172 2:1 0.110197 +0.035040 +0.221524 -0.542673 1:1 0.107477 +0.034451 +0.178295 -0.557495

Claim 49

A singlet lens, said lens having a radial index of refraction gradient according to an equation of the form N( Rho ) N00 + N10 Rho + N20 Rho 2 . . . , where, Rho y2 + z2 said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a thickness t 1.75 units, a focal length, F.L. 10.0 units, a starting value for the index of refraction N00 1.60, the relationship between CV1, CV2, and N10 and N20, the coefficients of the second and third terms of the index of refraction equation, respectively, as a function of object-image conjugates, is substantially given by the following table, and whereby at least the third-order spherical aberration, coma, and astigmatism of said lens are simultaneously reduced Thickness 1.75 Focal Length 10 N00 1.60 Conjugates N10 N20CV1 CV2 Infinity -0.992238 0.000117 +0.260641 +0.833375 20:1 -0.092900 0.000548 +0.250957 +0.816016 10:1 -0.093489 0.000935 +0.242169 +0.800673 5:1 -0.094462 0.001604 +0.226825 +0.774626 2:1 -0.096571 0.003021 +0.193687 +0.722555 1:1 -0.098693 0.004366 +0.161507 +0.677219

Claim 50

A singlet lens, said lens having a radial index of refraction gradient according to an equation of the form N( Rho ) N00 + N10 Rho + N20 Rho 2 . . . , where, Rho y2 + z2 said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a thickness t 1.75 units, a focal length, F.L. 10.0 units, a starting value for the index of refraction N00 1.60, the relationship between CV1, CV2, and N10 and N20, the coefficients of the second and third terms of the index of refraction equation, respectively, as a function of object-image conjugates, is substantially given by the following table, and whereby at least the third-order spherical aberration, coma, and astigmatism of said lens are simultaneously reduced Thickness 1.75 Focal Length 10 N00 1.60 Conjugates N10 N20CV1 CV2 Infinity -0.992238 0.000117 +0.260641 +0.833375 20:1 -0.092900 0.000548 +0.250957 +0.816016 10:1 -0.093489 0.000935 +0.242169 +0.800673 5:1 -0.094462 0.001604 +0.226825 +0.774626 2:1 -0.096571 0.003021 +0.193687 +0.722555 1:1 -0.098693 0.004366 +0.161507 +0.677219

Claim 51

A singlet lens, said lens having a radial index of refraction gradient according to an equation of the form N( Rho ) N00 + N10 Rho + N20 Rho 2 . . . , where, Rho y2 + z2 said lens further having a thickness t, a first curvature CV1, a second curvature CV2, wherein for a focal length, F.L. 10.0 units, a starting value for the index of refraction N00 1.60 and infinite conjugates, the relationship between CV1, CV2, and N10 and N20, the coefficients of the second and third terms of the index of refraction equation, respectively, as a function of the lens thickness t, is substantially given by the following table, and Whereby at least the third-order spherical aberration, coma, and astigmatism of said lens are simultaneously reduced Focal Length 10 Infinite Conjugates N00 1.60 Thickness N10 N20CV1 CV23.0 +0.045232 +0.006746 +0.252046 -0.354604 2.5 +0.061631 +0.011826 +0.252132 -0.409335 2.0 +0.090124 +0.023948 +0.251569 -0.488262 1.75 +0.126280 +0.042136 +0.374174 -0.502954

Claim 52

A singlet lens, said lens having a radial index of refraction gradient according to an equation of the form N( Rho ) N00 + N10 Rho + N20 Rho 2 . . . , where, Rho y2 + z2 said lens further having a thickness t, a first curvature CV1, a second curvature CV2, wherein for a focal length, F.L. 10.0 units, a starting value for the index of refraction N00 1.60 and infinite conjugates, the relationship between CV1, CV2, and N10 and N20, the coefficients of the second and third terms of the index of refraction equation, respectively, as a function of the lens thickness t, is substantially given by the following table, and Whereby at least the third-order spherical aberration, coma, and astigmatism of said lens are simultaneously reduced Focal Length 10 Infinite Conjugates N00 1.60 Thickness N10 N20CV1 CV23.0 +0.045232 +0.006746 +0.252046 -0.354604 2.5 +0.061631 +0.011826 +0.252132 -0.409335 2.0 +0.090124 +0.023948 +0.251569 -0.488262 1.75 +0.126280 +0.042136 +0.374174 -0.502954

Claim 53

A singlet lens having a radial index of refraction gradient according to an equation of the form N( Rho ) N00 + N10 Rho + N20 Rho 2 . . . , where Rho y2 + z2 said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a focal length F.L. 10.0 units, a starting value for the index of refraction N00 1.60 and infinite conjugates, the relationship between CV1, CV2, and N10 and N20, the coefficients of the second and third terms of the index of refraction equation, respectively, as a function of the lens thickness t, is substantially given by the following table, and whereby at least the third-order spherical aberration, coma, and astigmatism of said lens are simultaneously reduced Focal Length 10 Infinite Conjugates N00 1.60 Thickness N10 N20CV1 CV23.0 -0.047735 -0.000605 +0.209069 +0.803016 2.5 -0.059577 -0.000586 +0.224043 +0.800711 2.0 -0.078299 -0.000308 +0.245681 +0.816579 1.75 -0.092238 +0.000117 +0.260641 +0.833875 1.50 -0.111418 +0.001031 +0.280029 +0.858299 1.00 -0.182527 +0.008065 +0.343729 +0.947781

Claim 54

A singlet lens having a radial index of refraction gradient according to an equation of the form N( Rho ) N00 + N10 Rho + N20 Rho 2 . . . , where Rho y2 + z2 said lens further having a thickness t, a first curvature CV1, and a second curvature CV2, wherein for a focal length F.L. 10.0 units, a starting value for the index of refraction N00 1.60 and infinite conjugates, the relationship between CV1, CV2, and N10 and N20, the coefficients of the second and third terms of the index of refraction equation, respectively, as a function of the lens thickness t, is substantially given by the following table, and whereby at least the third-order spherical aberration, coma, and astigmatism of said lens are simultaneously reduced Focal Length 10 Infinite Conjugates N00 1.60 Thickness N10 N20CV1 CV23.0 -0.047735 -0.000605 +0.209069 +0.803016 2.5 -0.059577 -0.000586 +0.224043 +0.800711 2.0 -0.078299 -0.000308 +0.245681 +0.816579 1.75 -0.092238 +0.000117 +0.260641 +0.833875 1.50 -0.111418 +0.001031 +0.280029 +0.858299 1.00 -0.182527 +0.008065 +0.343729 +0.947781

Claim 55

A singlet lens having plane parallel surfaces comprised of glass having a radial index of refraction gradient given by an equation of the form N( Rho ) N00 + N10 Rho N20 Rho 2 + . . . , where, Rho y2 + z2, said lens having a thickness t units, an object to lens distance Do units, an image to lens distance Di units, a starting value for the index of refraction N00 1.5, wherein for a lens having at least the third-order spherical aberration reduced, the relationship between N10 and N20, the second and third coefficients, respectively, of the index of refraction equation, and t, Do, and Di, are as substantially set forth in the following table, and interpolations and extrapolations thereof Dot DiN10 N20Infinite 1.000 -100.00 0.005011 -0.000000 Infinite 1.000 -50.00 0.010045 -0.000001 Infinite 1.000 - 10.00 0.051131 -0.000176 Infinite 1.000 - 2.50 0.219107 -0.014349 Infinite 1.000 2.50 -0.183424 0.007509 Infinite 1.000 10.00 -0.048908 0.000149 Infinite 1.000 50.00 -0.009956 0.000001 Infinite 1.000 100.00 -0.004989 0.000000 -40.00 1.000 10.00 -0.036064 0.000145 -20.00 1.000 10.00 -0.023076 0.000125 -8.00 1.000 10.00 0.016760 -0.000218 -4.00 1.000 10.00 0.086184 -0.003062 - 2.00 1.000 10.00 0.237331 -0.031119 2.00 1.000 10.00 -0.0278570 0.014309 4.00 1.000 10.00 -0.169914 0.002319 8.00 1.000 10.00 -0.111058 0.000455 Infinite 0.100 10.00 -0.498891 0.001607 Infinite 0.250 10.00 -0.198894 0.000635 Infinite 0.500 10.00 -0.098899 0.000311 Infinite 1.000 10.00 -0.048908 0.000149 Infinite 2.000 10.00 -0.023927 0.000069

Claim 56

A singlet lens having plane parallel surfaces comprised of glass having a radial index of refraction gradient given by an equation of the form N( Rho ) N00 + N10 Rho N20 Rho 2 + . . . , where, Rho y2 + z2, said lens having a thickness t units, an object to lens distance Do units, an image to lens distance Di units, a starting value for the index of refraction N00 1.5, wherein for a lens having at least the third-order spherical aberration reduced, the relationship between N10 and N20, the second and third coefficients, respectively, of the index of refraction equation, and t, Do, and Di, are as substantially set forth in the following table, and interpolations and extrapolations thereof Dot DiN10 N20Infinite 1.000 -100.00 0.005011 -0.000000 Infinite 1.000 -50.00 0.010045 -0.000001 Infinite 1.000 - 10.00 0.051131 -0.000176 Infinite 1.000 - 2.50 0.219107 -0.014349 Infinite 1.000 2.50 -0.183424 0.007509 Infinite 1.000 10.00 -0.048908 0.000149 Infinite 1.000 50.00 -0.009956 0.000001 Infinite 1.000 100.00 -0.004989 0.000000 -40.00 1.000 10.00 -0.036064 0.000145 -20.00 1.000 10.00 -0.023076 0.000125 -8.00 1.000 10.00 0.016760 -0.000218 -4.00 1.000 10.00 0.086184 -0.003062 - 2.00 1.000 10.00 0.237331 -0.031119 2.00 1.000 10.00 -0.0278570 0.014309 4.00 1.000 10.00 -0.169914 0.002319 8.00 1.000 10.00 -0.111058 0.000455 Infinite 0.100 10.00 -0.498891 0.001607 Infinite 0.250 10.00 -0.198894 0.000635 Infinite 0.500 10.00 -0.098899 0.000311 Infinite 1.000 10.00 -0.048908 0.000149 Infinite 2.000 10.00 -0.023927 0.000069