Eyeglass lens

An eyeglass lens at least one surface of which is a refracting surface arranged such that two coordinate axes x and Y are set to contact with the refracting surface at a determined point thereon while directions of the coordinate axes and an XY plane including the two axes are determined, that a perpendicular line is dropped toward the XY plane from an arbitrary point on the refracting surface, and then X, Y coordinates of an intersecting point between the perpendicular line and the XY plane are denoted by x and y, respectively, and the length of the perpendicular line by z, and that a value of z is expressed as follows:

• ##EQU18## where C.sub.x, C.sub.y, K.sub.x, K.sub.y, B.sub.m,j are constants to define the shape of lens;
• m, j are integers satisfying conditions of 0.ltoreq.m, 0.ltoreq.j, and 1.ltoreq.m+j;
• coefficients satisfy the following conditions:
• .vertline.B.sub.m,j .vertline..ltoreq.10.sup.-2(m+j) ( 6)
• which cannot be simultaneously zero.

An eyeglass lens at least one surface of which is a refracting surface arranged such that two coordinate axes X and Y are set to contact with the refracting surface at a determined point thereon while directions of the coordinate axes and an XY plane including the two axes are determined, that a perpendicular line is dropped toward the XY plane from an arbitrary point on the refracting surface, and then X, Y coordinates of an intersecting point between the perpendicular line and the XY plane are denoted by x and y, respectively, and the length of the perpendicular line by z, and that a value of z is expressed as follows:

• ##EQU19## where r.sup.2 =x.sup.2 +y.sup.2 ;
• C.sub.x, C.sub.y, K.sub.x, K.sub.y, D.sub.n, E.sub.n are constants to define the shape of lens;
• n is an integer satisfying a condition of 2.ltoreq.n;
• coefficients satisfy the following conditions:
• .vertline.D.sub.n .vertline..ltoreq.10.sup.-n ( 8),
• .vertline.E.sub.n .vertline..ltoreq.10.sup.-n ( 9),
• which cannot be simultaneously zero.

An eyeglass lens in which a front refracting surface on the object side (as will be referred to as a first surface) is a refracting surface having a shape as expressed by Equation (1) , (5), or (7) ##EQU20## where r.sup.2 =x.sup.2 +y.sup.2 ;

• C.sub.x, C.sub.y, K.sub.x, K.sub.y, A.sub.n,m,j are constants to define the shape of lens;
• n, m, j are integers satisfying conditions of 2.ltoreq.n, 0.ltoreq.m, 0.ltoreq.j, and 1.ltoreq.m+j;
• coefficients satisfy the following conditions:
• ##EQU21## which cannot be simultaneously zero, ##EQU22## where C.sub.x, C.sub.y, K.sub.x, K.sub.y, B.sub.m,j are constants to define the shape of lens;
• m, j are integers satisfying conditions of 0.ltoreq.m, 0.ltoreq.j, and 1.ltoreq.m+j;
• coefficients satisfy the following conditions:
• .vertline.B.sub.m,j .vertline..ltoreq.10.sup.-2(m+j) ( 6),
• which cannot be simultaneously zero), or ##EQU23## where r.sup.2 =x.sup.2 +y.sup.2 ;
• C.sub.x, C.sub.y, K.sub.x, K.sub.y, D.sub.n, E.sub.n are constants to define the shape of lens;
• n is an integer satisfying a condition of 2.ltoreq.n;
• coefficients satisfy the following conditions:
• .vertline.D.sub.n .vertline..ltoreq.10.sup.-n ( 8),
• .vertline.E.sub.n .vertline..ltoreq.10.sup.-n ( 9),
• which cannot be simultaneously zero (as will be referred to as an extended toric surface) and a rear refracting surface on the eyeball side (as will be referred to as a second surface) is a spherical or toric surface, which has a positive refracting power defined as follows:
• when the first surface is cut by a plane including the X axis and the Z axis a curve appearing in a cut surface has a radius of curvature R1.sub.x (mm) at the coordinate origin, and when the first surface is cut by a plane including the Y axis and the Z axis a curve appearing in a cut surface has a radius of curvature R1.sub.y (mm) at the coordinate origin;
• similarly, when the second surface is cut by a plane including the X axis and the Z axis a curve appearing in a cut surface has a radius of curvature R2.sub.x (mm) at the coordinate origin, and when the second surface is cut by a plane including the Y axis and the Z axis a curve appearing in a cut surface has a radius of curvature R2.sub.y (mm) at the coordinate origin;
• (where signs are determined as "+" when the curvature center is on the eyeball side with respect to the refracting surface and "-" when it is on the object side;)
• an index of refraction of lens medium is N;
• refracting powers of the first surface, S1.sub.x (Diopter as will be abbreviated as "D") and S1.sub.y (D), and refracting powers of the second surface, S2.sub.x (D) and S2.sub.y (D) are defined by the following equations:
• ##EQU24## in which max
• (S2.sub.x, S2.sub.y).ltoreq.min (S1.sub.x, S1.sub.y) (14)
• (where max (a, b) represents a larger one of a and b and min (a, b) is a smaller one of a and b);
• and further in which, defining G.sub.x and G.sub.y as follows depending upon the representation equation of the extended toric surface of the lens:
• G.sub.x =.SIGMA.A.sub.4,m,0,G.sub.y =.SIGMA.A.sub.4,0,j ( 15);
• or
• G.sub.x =B.sub.2,0, G.sub.y =B.sub.0,2 ( 16);
• or
• G.sub.x =D.sub.4,G.sub.y =E.sub.4 ( 17),
• the following conditions are satisfied:
• K.sub.x +8R1.sub.x.sup.3 G.sub.x .ltoreq.1.0 (18);
• K.sub.y +8R1.sub.y.sup.3 G.sub.y .ltoreq.1.0 (19).

An eyeglass lens in which the first surface is a spherical or toric surface and the second surface is an extended toric surface as expressed by Equation (1), (5), or (7) ##EQU25## where r.sup.2 =x.sup.2 +y.sup.2 ;

• C.sub.x, C.sub.y, K.sub.x, K.sub.y, A.sub.n,m,j are constants to define the shape of lens;
• n, m, j are integers satisfying conditions of 2.ltoreq.n, 0.ltoreq.m, 0.ltoreq.j, and 1.ltoreq.m+j;
• coefficients satisfy the following conditions:
• ##EQU26## which cannot be simultaneously zero, ##EQU27## where C.sub.x, C.sub.y, K.sub.x, K.sub.y, B.sub.m,j are constants to define the shape of lens;
• m, j are integers satisfying conditions of 0.ltoreq.m, 0.ltoreq.j, and 1.ltoreq.m+j;
• coefficients satisfy the following conditions:
• .vertline.B.sub.m,j .vertline..ltoreq.10.sup.-2(m+j) ( 6),
• which cannot be simultaneously zero, or ##EQU28## where r.sup.2 =x.sup.2 +y.sup.2 ;
• C.sub.x, C.sub.y, K.sub.x, K.sub.y, D.sub.n, E.sub.n are constants to define the shape of lens;
• n is an integer satisfying a condition of 2.ltoreq.n;
• coefficients satisfy the following conditions:
• .vertline.D.sub.n .vertline..ltoreq.10.sup.-n ( 8),
• .vertline.E.sub.n .vertline..ltoreq.10.sup.-n ( 9),
• which cannot be simultaneously zero
• which has such a positive refracting power that refracting powers S1.sub.x (D) and S1.sub.y (D) of the first surface and refracting powers S2.sub.x (D) and S2.sub.y (D) of the second surface are defined by Equations (10) to (13) ##EQU29## and that Equation (14) in which max
• (S2.sub.x, S2.sub.y).ltoreq.min(S1.sub.x, S1.sub.y) (14)
• (where max (a, b) represents a larger one of a and b and min (a,b) is a smaller one of a and b);
• stands, and in which, defining G.sub.x and G.sub.y by Equations (15) to (17)
• G.sub.x =.SIGMA.A.sub.4,m,0, G.sub.y =.SIGMA.A.sub.4,0,j ( 15);
• or
• G.sub.x =B.sub.2,0,G.sub.y =B.sub.0,2 ( 16);
• or
• G.sub.x =D.sub.4,G.sub.y =E.sub.4 ( 17),
• the following conditions are satisfied:
• K.sub.x +8R1.sub.x.sup.3 G.sub.x .ltoreq.1.0 (18);
• K.sub.y +8R1.sub.y.sup.3 G.sub.y .ltoreq.1.0 (19)
• depending upon the representation equation of the extended toric surface of the lens, the following conditions are satisfied:
• -1. 0.ltoreq.K.sub.x +8R2.sub.x.sup.3 G.sub.x ( 20);
• -1.0.ltoreq.K.sub.y +8R2.sub.y.sup.3 G.sub.y ( 21).

An eyeglass lens in which a first surface is an extended toric surface of the shape as expressed by Equation (1), (5), or (7) ##EQU30## where r.sup.2 =x.sup.2 +y.sup.2 ;

• C.sub.x, C.sub.y, K.sub.x, K.sub.y, A.sub.n,m,j are constants to define the shade of lens;
• n, m, j are integers satisfying conditions of 2.ltoreq.n, 0.ltoreq.m, 0.ltoreq.j, and 1.ltoreq.m+j;
• coefficients satisfy the following conditions:
• ##EQU31## which cannot be simultaneously zero, ##EQU32## where C.sub.x, C.sub.y, K.sub.x, K.sub.y, B.sub.m,j are constants to define the shape of lens;
• m, j are integers satisfying conditions of 0.ltoreq.m, 0.ltoreq.j, and 1.ltoreq.m+j;
• coefficients satisfy the following conditions:
• .vertline.B.sub.m,j .vertline..ltoreq.10.sup.-2(m+j) ( 6),
• which cannot be simultaneously zero, or ##EQU33## where r.sup.2 =x.sup.2 +y.sup.2 ;
• C.sub.x, C.sub.y, K.sub.x, K.sub.y, D.sub.n, E.sub.n are constants to define the shape of lens;
• n is an integer satisfying a condition of 2.ltoreq.n;
• coefficients satisfy the following conditions:
• .vertline.D.sub.n .vertline..ltoreq.10.sup.-n ( 8),
• .vertline.E.sub.n .vertline..ltoreq.10.sup.-n ( 9),
• which cannot be simultaneously zero and a second surface is a spherical or toric surface, which has such a negative refracting power that refracting powers S1.sub.x (D) and S1.sub.y (D) of the first surface and refracting powers S2.sub.x (D) and S2.sub.y (D) of the second surface are defined by Equation (10) to (13) ##EQU34## and that the following equation stands:
• max (S1.sub.x, S1.sub.y).ltoreq.min(S2.sub.x, S2.sub.y) (22),
• and in which, defining G.sub.x and G.sub.y by Equations (15) to (17)
• G.sub.x =.SIGMA.A.sub.4,m,0,G.sub.y =.SIGMA.A.sub.4,0,j ( 15);
• G.sub.x =B.sub.2,0,G.sub.y =B.sub.0,2 ( 16);
• or
• G.sub.x =D.sub.4,G.sub.y =E.sub.4 ( 17),
• depending upon the representation equation of the extended toric surface of the lens, the following conditions are satisfied:
• -1. 0.ltoreq.K.sub.x +8R1.sub.x 3G.sub.x ( 23);
• -1.0.ltoreq.K.sub.y +8R1.sub.y 3G.sub.y ( 24).

An eyeglass lens in which a first surface is a spherical or toric surface and a second surface is an extended toric surface of the shape as expressed by Equation (1), (5), or (7) ##EQU35## where r.sup.2 =x.sup.2 +y.sup.2 ;

• C.sub.x, C.sub.y, K.sub.x, K.sub.y, A.sub.n,m,j are constants to define the shape of lens;
• n, m, j are integers satisfying conditions of 2.ltoreq.n, 0.ltoreq.m, 0.ltoreq.j, and 1.ltoreq.m+j;
• coefficients satisfy the following conditions:
• ##EQU36## which cannot be simultaneously zero, ##EQU37## where C.sub.x, C.sub.y, K.sub.x, K.sub.y, B.sub.m,j are constants to define the shape of lens;
• m, j are integers satisfying conditions of 0.ltoreq.m, 0.ltoreq.j, and 1.ltoreq.m+j;
• coefficients satisfy the following conditions:
• .vertline.B.sub.m,j .vertline..ltoreq.10.sup.-2(m+j) ( 6),
• which cannot be simultaneously zero, or ##EQU38## where r.sup.2 =x.sup.2 +y.sup.2 ;
• C.sub.x, C.sub.y, K.sub.x, K.sub.y, D.sub.n, E.sub.n are constants to define the shape of lens;
• n is an integer satisfying a condition of 2.ltoreq.n;
• coefficients satisfy the following conditions:
• .vertline.D.sub.n .vertline..ltoreq.10.sup.-n ( 8),
• .vertline.E.sub.n .vertline..ltoreq.10.sup.-n ( 9),
• which cannot be simultaneously zero which has such a negative refracting power that refracting powers S1.sub.x (D) and S1.sub.y (D) of the first surface and refracting powers S2.sub.x (D) and S2.sub.y (D) of the second surface are defined by Equations (10) to (13) ##EQU39## and that Equation (22)
• max(S1.sub.x, S1.sub.y).ltoreq.min(S2.sub.x,S2.sub.y) (22)
• stands, and in which, defining G.sub.x and G.sub.y by Equations (15) to (17)
• G.sub.x =.SIGMA.A.sub.4,m,0,G.sub.y =.SIGMA.A.sub.4,0,j ( 15);
• or
• G.sub.x =B.sub.2,0,G.sub.y =B.sub.0,2 ( 16);
• or
• G.sub.x =D.sub.4,G.sub.y =E.sub.4 ( 17),
• depending upon the representation equation of the extended toric surface of the lens, the following conditions are satisfied:
• K.sub.x +8R2.sub.x.sup.3 G.sub.x .ltoreq.1.0 (25);
• K.sub.y +8R2.sub.y.sup.3 G.sub.y .ltoreq.1.0 (26).

An eyeglass lens having two refracting surfaces, one of which is an extended toric surface of the shape as expressed by Equation (1), (5), or (7) ##EQU40## where r.sup.2 =x.sup.2 +y.sup.2 ;

• C.sub.x, C.sub.y, K.sub.x, K.sub.y, A.sub.n,m,j are constants to define the shape of lens;
• n, m, j are integers satisfying conditions of 2.ltoreq.n, 0.ltoreq.m, 0.ltoreq.j, and 1.ltoreq.m+j;
• coefficients satisfy the following conditions:
• ##EQU41## which cannot be simultaneously zero, ##EQU42## where C.sub.x, C.sub.y, K.sub.x, K.sub.y, B.sub.m,j are constants to define the shape of lens;
• m, j are integers satisfying conditions of 0.ltoreq.m, 0.ltoreq.j, and 1.ltoreq.m+j;
• coefficients satisfy the following conditions:
• .vertline.B.sub.m,j .vertline..ltoreq.10.sup.-2(m+j) ( 6),
• which cannot be simultaneously zero, or ##EQU43## where r.sup.2 =x.sup.2 +y.sup.2 ;
• C.sub.x, C.sub.y, K.sub.x, K.sub.y, D.sub.n, E.sub.n are constants to define the shade of lens;
• n is an integer satisfying a condition of 2.ltoreq.n;
• coefficients satisfy the following conditions:
• .vertline.D.sub.n .vertline..ltoreq.10.sup.-n ( 8),
• .vertline.E.sub.n .vertline..ltoreq.10.sup.-n ( 9),
• which cannot be simultaneously zero and the other of which is an axially symmetric aspherical surface, said extended toric surface having at the origin a radius of curvature R.sub.x in the X direction and a radius of curvature R.sub.y in the Y direction which satisfy the following conditions:
• K.sub.y +8R.sub.x.sup.3 G.sub.x .ltoreq.2.0 (27);
• or
• K.sub.y +8R.sub.y.sup.3 G.sub.y .ltoreq.2.0 (28),
• where G.sub.x and G.sub.y are defined by Equations (15) to (17)
• G.sub.x =.SIGMA.A.sub.4,m,0,G.sub.y =.SIGMA.A.sub.4,0,j ( 15);
• or
• G.sub.x =B.sub.2,0,G.sub.y =B.sub.0,2 ( 16);
• or
• G.sub.x =D.sub.4,G.sub.y =E.sub.4 ( 17),

An eyeglass lens in which at least one of a first surface and a second, opposite-side surface of the lens is divided into a plurality of regions, each of the regions being constructed by an extended toric surface of the shape as expressed by ##EQU44## where r.sup.2 =x.sup.2 +y.sup.2 ;

• C.sub.x, C.sub.y, K.sub.x, K.sub.y, A.sub.n,m,j are constants to define the shape of lens;
• n, m, j are integers satisfying conditions of 2.ltoreq.n, 0.ltoreq.m, 0.ltoreq.j, and 1.ltoreq.m+j;
• coefficients satisfy the following conditions:
• ##EQU45## which cannot be simultaneously zero, ##EQU46## where C.sub.x, C.sub.y, K.sub.x, K.sub.y, B.sub.m,j are constants to define the shape of lens;
• m, j are integers satisfying conditions of 0.ltoreq.m, 0.ltoreq.j, and 1.ltoreq.m+j;
• coefficients satisfy the following conditions:
• .vertline.B.sub.m,j .vertline..ltoreq.10.sup.-2(m+j) ( 6),
• which cannot be simultaneously zero, or ##EQU47## where r.sup.2 =x.sup.2 +y.sup.2 ;
• C.sub.x, C.sub.y, K.sub.x, K.sub.y, D.sub.n, E.sub.n are constants to define the shape of lens;
• n is an integer satisfying a condition of 2.ltoreq.n;
• coefficients satisfy the following conditions:
• .vertline.D.sub.n .vertline..ltoreq.10.sup.-n ( 8),
• .vertline.E.sub.n .vertline..ltoreq.10.sup.-n ( 9),
• which cannot be simultaneously zero
• at least one of the coefficients in the equations (1), (5) and (7) having a different value in each of the regions so that each divided region has different aberration.