US4676610A — Method of making progressive lens surface and res…

Claim 1

Independent Claim 166 words

A method for making an optical body having a distance viewing zone, a near viewing zone, and an intermediate zone in which there is a gradual change in optical power from the distance zone to the near zone, comprising the steps of: selecting a base surface function Z d progenitive of prescribed optical properties in the distance zone; selecting a deviation function Z representative in value of a deviation from the base surface in the intermediate zone, said deviation function having a zero value in the distance zone and having a value in the intermediate zone given by a polynomial function in a two dimensional curvilinear coordinate system (u,v), boundaries of the zones in the coordinate system being defined so that, along the eye path, u equals a constant, and so that, along a distance zone boundary and a near zone boundary, v equals a constant; and forming a lens surface in the optical body responsive to a surface function Z T where Z.sub.T =Z.sub.d +Z.

Claim 2

Independent Claim 166 words

A method for making an optical body having a distance viewing zone, a near viewing zone, and an intermediate zone in which there is a gradual change in optical power from the distance zone to the near zone, comprising the steps of: selecting a base surface function Z d progenitive of prescribed optical properties in the distance zone; selecting a deviation function Z representative in value of a deviation from the base surface in the intermediate zone, said deviation function having a zero value in the distance zone and having a value in the intermediate zone given by a polynomial function in a two dimensional curvilinear coordinate system (u,v), boundaries of the zones in the coordinate system being defined so that, along the eye path, u equals a constant, and so that, along a distance zone boundary and a near zone boundary, v equals a constant; and forming a lens surface in the optical body responsive to a surface function Z T where Z.sub.T =Z.sub.d +Z.

Claim 3

Dependent Claim 60 words

The method of claim 1 wherein the polynomial function is defined by an equation of the form: ##EQU8## where n and m are degrees of u and v, respectively; where A ij is a set of constants; and where u i and v i are the coordinates of the curvilinear coordinate system, raised to the ith and jth power, respectively.

Claim 4

Dependent Claim 18 words

The method of claim 2 wherein n and m are each integers less than or equal to 8.

Claim 5

Dependent Claim 63 words

The method of claim 3 wherein u and v are defined such that the cartesian coordinates x and y are given by transformation equations of the form: ##EQU9## where p and q are degrees of u and v defining x, where r and s are degrees of u and v defining y; and where X ij and Y ij are sets of constants.

Claim 6

Dependent Claim 20 words

The method of claim 4 wherein p, q, r and s are each integers less than or equal to 2.

Claim 7

Dependent Claim 283 words

A multifocal, progressive lens with a lens surface having a near viewing zone, a distance viewing zone, and an intermediate zone in which there is a gradual change in optical power along an eye path from the distance zone to the near zone; wherein boundaries between the distance zone and the intermediate zone, and between the intermediate zone and near zone are substantially projections of algebraic curves on the lens surface; and wherein the shape of the surface of the lens is substantially defined by a final surface function such that the surfaces of the zones are the same height at the boundaries and so that at least the first three derivatives of the final surface function are continuous across the boundaries, wherein the function is defined by an equation of the form: Z.sub.T =Z.sub.d +Z wherein Z T is the final surface function, Z d is the surface of the distance zone extended over the entire optical body and Z is defined in the intermediate zone by an equation of the form: ##EQU10## where n and m are integers less than 10, where A ij are a set of constants and where u i and v j are coordinates of a curvilinear coordinate system, raised to the ith and jth power, respectively, u and v being defined such that the cartesian coordinates x and y are given by transformation equations of the form: ##EQU11## where p, q, r and s are each integers less than or equal to 2; and where X ij and Y ij are further sets of constants, and, wherein, a near zone portion of the function Z is a polynomial function in the cartesian coordinates x and y.

Claim 8

Dependent Claim 283 words

A multifocal, progressive lens with a lens surface having a near viewing zone, a distance viewing zone, and an intermediate zone in which there is a gradual change in optical power along an eye path from the distance zone to the near zone; wherein boundaries between the distance zone and the intermediate zone, and between the intermediate zone and near zone are substantially projections of algebraic curves on the lens surface; and wherein the shape of the surface of the lens is substantially defined by a final surface function such that the surfaces of the zones are the same height at the boundaries and so that at least the first three derivatives of the final surface function are continuous across the boundaries, wherein the function is defined by an equation of the form: Z.sub.T =Z.sub.d +Z wherein Z T is the final surface function, Z d is the surface of the distance zone extended over the entire optical body and Z is defined in the intermediate zone by an equation of the form: ##EQU10## where n and m are integers less than 10, where A ij are a set of constants and where u i and v j are coordinates of a curvilinear coordinate system, raised to the ith and jth power, respectively, u and v being defined such that the cartesian coordinates x and y are given by transformation equations of the form: ##EQU11## where p, q, r and s are each integers less than or equal to 2; and where X ij and Y ij are further sets of constants, and, wherein, a near zone portion of the function Z is a polynomial function in the cartesian coordinates x and y.

Claim 9

Dependent Claim 31 words

The lens of claim 6 wherein the surface of the distance zone is rotationally symmetric about an axis substantially perpendicular to an x-y plane of the cartesian coordinates x and y.

Claim 10

Dependent Claim 16 words

The lens of claim 7 wherein the rotationally symmetric surface of the distance zone is spherical.

Claim 11

Dependent Claim 21 words

The lens of claim 8 wherein the vertex of the distance zone is located at the approximate center of the lens.

Claim 12

Dependent Claim 12 words

The lens of claim 6 wherein both the algebraic curves are parabolas.

Claim 13

Dependent Claim 11 words

The lens of claim 6 wherein Z=0 in the distance zone.

Claim 14

Dependent Claim 28 words

The lens of claim 6 wherein the transformation equations are given by: x=(c/v.sub.o)(v+v.sub.1)(v.sub.o -v.sub.1 -v)(au.sup.2 +1)+u y=(v+v.sub.1)(au.sup.2 +1) wherein a, c, v o and v 1 are constants.

Claim 15

Dependent Claim 52 words

The lens of claim 12 wherein the curve u=0 is the eye path; the curve v=0 is the boundary between the distance and the intermediate zones; v o and c are parameters which determine a nasal offset of the near zone boundary; and the constant, a, determines the curvatures of the boundaries.

Claim 16

Dependent Claim 37 words

The lens of claim 13 wherein: a is from 0 to 1 mm -2 ; c is from -1 to 1; v o is greater than 1 mm; and v 1 is from -100 to 100 mm.

Claim 17

Dependent Claim 34 words

The lens of claim 6 wherein the final surface function is the sum of the function Z d and the function Z which is the product of a preliminary function and an auxiliary function.

Claim 18

Dependent Claim 43 words

The lens of claim 15 wherein the function Z d is a surface of the distance zone extended over the entire lens, said surface being rotationally symmetric about an axis substantially perpendicular to an x-y plane of the cartesian coordinates x and y.

Claim 19

Dependent Claim 43 words

The lens of claim 15 wherein the preliminary function is selected so that the surfaces of the zones are the same height at the boundaries and so that at least the first three derivatives of the preliminary function are continuous across the boundaries.

Claim 20

Dependent Claim 20 words

The lens of claim 15 wherein the auxiliary function is continuous in all derivatives up to and including the third.

Claim 21

Dependent Claim 20 words

The lens of claim 15 wherein the auxiliary function distributes, in a predetermined fashion, astigmatism correction in the intermediate zone.

Claim 22

Dependent Claim 29 words

The lens of claim 19 wherein the auxiliary function is a function S(y) given by an equation of the form: ##EQU12## where Y c and σ y are constants.

Claim 23

Dependent Claim 20 words

The lens of claim 15 wherein the auxiliary function distributes, in a predetermined fashion, orthoscopic correction in the intermediate zone.

Claim 24

Dependent Claim 31 words

The lens of claim 21 wherein the auxiliary function is a function U(u) given by an equation of the form: U(u)=e.sup.- (u/σ.sub.u).sup.4 for all u, where σ u is a constant.

Claim 25

Dependent Claim 88 words

The lens of claim 6 wherein the surface of the near zone is defined by an equation of the form: Z.sub.T =Z.sub.d +Z.sub.s where Z T is the final function, Z d is the rotationally symmetric surface of the distance zone extended over the entire lens, and Z s is a near zone surface function given by an equation of the form: Z.sub.s =A.sub.s [(x-x.sub.o).sup.2 +(y-y.sub.o).sup.2 ]+B.sub.s [(x-x.sub.o).sup.2 +(y-y.sub.o).sup.2 ].sup.2 +z.sub.o where A s , B s , x o , y o and z o are constants.

Claim 26

Dependent Claim 194 words

A multifocal, progressive lens with a lens surface having a near viewing zone, a distance viewing zone which is rotationally symmetric, and an intermediate zone in which there is a gradual change in optical power along an eye path from the distance zone to the near zone; wherein boundaries defined between the distance zone and the intermediate zone, and between the intermediate zone and near zone are substantially projections of algebraic curves on the lens surface; and wherein the shape of the surface of the lens is substantially defined by a final surface function such that the surfaces of the zones are the same height at the boundaries and so that at least the first three derivatives of the final surface function are continuous across the boundaries, wherein the surface of the near zone is defined by an equation of the form Z T =Z d +Z s where Z T is the final function, Z d is the surface of the distance zone extended over the entire lens and Z s is a near zone surface function having a factor given by a fourth degree expression in the cartesian coordinates x and y.

Claim 27

Dependent Claim 194 words

A multifocal, progressive lens with a lens surface having a near viewing zone, a distance viewing zone which is rotationally symmetric, and an intermediate zone in which there is a gradual change in optical power along an eye path from the distance zone to the near zone; wherein boundaries defined between the distance zone and the intermediate zone, and between the intermediate zone and near zone are substantially projections of algebraic curves on the lens surface; and wherein the shape of the surface of the lens is substantially defined by a final surface function such that the surfaces of the zones are the same height at the boundaries and so that at least the first three derivatives of the final surface function are continuous across the boundaries, wherein the surface of the near zone is defined by an equation of the form Z T =Z d +Z s where Z T is the final function, Z d is the surface of the distance zone extended over the entire lens and Z s is a near zone surface function having a factor given by a fourth degree expression in the cartesian coordinates x and y.

Claim 28

Dependent Claim 41 words

The lens of claim 24 wherein the factor is given by an expression of the form A.sub.s [(x-x.sub.o).sup.2 +(y-y.sub.o).sup.2 ]+B.sub.s [(x-x.sub.o).sup.2 +(y-y.sub.o).sup.2 ].sup.2 +z.sub.o wherein A s , B s , x o , y o and z o are constants.

Claim 29

Dependent Claim 131 words

A former for a multifocal, progressive lens with a progressive surface progenitive of a near viewing zone, a distance viewing zone which is rotationally symmetric, and an intermediate zone in which there is a gradual change in optical power along an eye path from the distance zone to the near zone; wherein boundaries are defined between the distance zone and the intermediate zone, and between the intermediate zone and near zone which are projections of algebraic curves on the surface; and wherein the shape of the surface is defined by a final surface function such that the surfaces of the zones are the same height along both of the boundaries and so that at least the first three derivatives of the final surface function are continuous across both of the boundaries.

Claim 30

Dependent Claim 131 words

A former for a multifocal, progressive lens with a progressive surface progenitive of a near viewing zone, a distance viewing zone which is rotationally symmetric, and an intermediate zone in which there is a gradual change in optical power along an eye path from the distance zone to the near zone; wherein boundaries are defined between the distance zone and the intermediate zone, and between the intermediate zone and near zone which are projections of algebraic curves on the surface; and wherein the shape of the surface is defined by a final surface function such that the surfaces of the zones are the same height along both of the boundaries and so that at least the first three derivatives of the final surface function are continuous across both of the boundaries.

Claim 31

Dependent Claim 83 words

The former of claim 26 wherein the surface is defined in the three zones by the function Z T given by an equation of the form: Z.sub.T =Z.sub.d +Z wherein Z d is a function defining a surface which provides prescribed optical properties in the distance zone, and Z is a deviation function representative in value of a deviation from Z d , said deviation function having a zero value in the distance zone and non-zero values in the near and intermediate zones.

Claim 32

Dependent Claim 117 words

The former of claim 27 wherein a factor of the function Z in the intermediate zone is defined by an expression of the form: ##EQU13## where n and m are each integers less than or equal to 8, where A ij is a set of constants and where u i and v j are coordinates of a curvilinear coordinate system, raised to the ith and jth power, respectively, u and v being defined such that the cartesian coordinates x and y are given by transformation equations of the form: ##EQU14## where p, q, r and s are each integers less than or equal to 2, and where X ij and Y ij are further sets of constants.

Claim 33

Dependent Claim 28 words

The former of claim 28 wherein the transformation equations are given by: x=(c/v.sub.o)(v+v.sub.1)(v.sub.o -v.sub.1 -v)(au.sup.2 +1)+u y=(v+v.sub.1)(au.sup.2 +1) wherein a, c, v o and v 1 are constants.

Claim 34

Dependent Claim 52 words

The former of claim 29 wherein the curve u=0 is the eye path; the curve v=0 is the boundary between the distance and the intermediate zones; v o and c are parameters which determine a nasal offset of the near zone boundary; and the constant, a, determines the curvatures of the boundaries.

Claim 35

Dependent Claim 37 words

The former of claim 30 wherein: a is from 0 to 1 mm -2 ; c is from -1 to 1; v o is greater than 1 mm; and v 1 is from -100 to 100 mm.

Claim 36

Dependent Claim 25 words

The former of claim 30 wherein the surface height along the eye path is substantially determined by a function of the fifth degree of v.

Claim 37

Independent Claim 321 words

A method for making lens having a distance viewing zone, a near viewing zone and an intermediate zone lying between boundaries with the distance and near zones, in which, in the intermediate zone, there is a gradual change in optical power along an eye path from the distance zone to the near zone, comprising the steps of: (a) selecting a base surface defined by a mathematical function which provides prescribed optical properties in the distance zone; (b) selecting a two-dimensional curvilinear coordinate system (u, v) in which the eye path is defined by the limitation that along the eye path, u equals a constant and in which the distance zone boundary and the near zone boundary are defined by the limitation, v equals a constant; (c) defining a near zone add surface function, which when summed with the base surface function will define a surface approximating the prescribed optical properties in the near zone; (d) deriving a preliminary polynomial function in the coordinate system such that the preliminary function defines a surface for the intermediate zone so that the surfaces of the zones are the same height at the boundaries and so that at least the first two partial derivatives with respect to the surface functions in the three zones are the same at the boundaries; (e) choosing an auxiliary function; (f) obtaining the product of the add surface function and the auxiliary function in the near zone; (g) obtaining the product of the preliminary function and the same auxiliary function in the intermediate zone; (h) adding the base surface function to the products of steps (f) and (g) in their respective zones to provide final surface functions defining the surface of the near zone and intermediate zone, respectively; and (i) forming the optical body with a surface substantially characterized, in the distance zone by the base surface function and, in the intermediate and near zones, by the final surface functions.

Claim 38

Independent Claim 321 words

A method for making lens having a distance viewing zone, a near viewing zone and an intermediate zone lying between boundaries with the distance and near zones, in which, in the intermediate zone, there is a gradual change in optical power along an eye path from the distance zone to the near zone, comprising the steps of: (a) selecting a base surface defined by a mathematical function which provides prescribed optical properties in the distance zone; (b) selecting a two-dimensional curvilinear coordinate system (u, v) in which the eye path is defined by the limitation that along the eye path, u equals a constant and in which the distance zone boundary and the near zone boundary are defined by the limitation, v equals a constant; (c) defining a near zone add surface function, which when summed with the base surface function will define a surface approximating the prescribed optical properties in the near zone; (d) deriving a preliminary polynomial function in the coordinate system such that the preliminary function defines a surface for the intermediate zone so that the surfaces of the zones are the same height at the boundaries and so that at least the first two partial derivatives with respect to the surface functions in the three zones are the same at the boundaries; (e) choosing an auxiliary function; (f) obtaining the product of the add surface function and the auxiliary function in the near zone; (g) obtaining the product of the preliminary function and the same auxiliary function in the intermediate zone; (h) adding the base surface function to the products of steps (f) and (g) in their respective zones to provide final surface functions defining the surface of the near zone and intermediate zone, respectively; and (i) forming the optical body with a surface substantially characterized, in the distance zone by the base surface function and, in the intermediate and near zones, by the final surface functions.

Claim 39

Dependent Claim 21 words

The method of claim 33 wherein the boundaries are defined as projections of parabolas on a surface of the optical body.

Claim 40

Dependent Claim 48 words

The method of claim 34 wherein the near zone add surface function Z s is given by an equation of the form Z.sub.s =A.sub.s [(x-x.sub.o).sup.2 +(y-y.sub.o).sup.2 ]+B.sub.s [(x-x.sub.o).sup.2 +(y-y.sub.o).sup.2 ].sup.2 +z.sub.o where A s , B s , x o , y o and z o are constants.

Claim 41

Dependent Claim 23 words

The method of claim 33 wherein the auxiliary function is chosen to reduce astigmatism in at least a portion of the intermediate zone.

Claim 42

Dependent Claim 23 words

The method of claim 33 wherein the auxiliary function is chosen to improve orthoscopy in at least a portion of the intermediate zone.

Claim 43

Dependent Claim 47 words

The method of claim 33 wherein the auxilliary function is, itself, the product of a function S(y) selected to reduce astigmatism in at least a portion of the intermediate zone, and a function U(u) selected to improve orthoscopy in at least a portion of the intermediate zone.

Claim 44

Dependent Claim 25 words

The method of claim 33 further comprising the step of using said optical body to profile a former for further formation of such optical bodies.

Claim 45

Independent Claim 278 words

A method for making an optical body having a distance viewing zone, a near viewing zone and an intermediate zone lying between boundaries with the distance and near zone, in which intermediate zone there is a gradual change in optical power along an eye path from the distance zone to the near zone, comprising the steps of: (a) selecting a rotationally symmetric base surface defined by a mathematical function which provides prescribed optical properties in the distance zone; (b) selecting a two dimensional coordinate system (u, v) in which, along the eye path, u equals a constant, and in which, along boundaries between the zones, v equals a constant; (c) defining a near zone add surface function, which, when summed with the base surface function, defines a surface approximating the prescribed optical properties in the near zone; (d) deriving a preliminary polynomial function in the coordinate system defining a surface for the intermediate zone such that the surfaces of the zones are the same height at the boundaries and such that at least the first three partial derivatives with respect to the surface functions in the three zones are the same at the boundaries; (e) adding the base surface function to the functions obtained in steps (c) and (d) in their respective zones to provide preliminary surface functions defining the surfaces of the near zones and intermediate zone, respectively; (f) evaluating the optical properties of the surface defined by the functions obtained in steps (a) and (e); (g) modifying the shape of the zone boundaries; (h) repeating steps (b) through (e) to obtain final surface functions; and (i) forming the optical body responsive to said final surface functions.

Claim 46

Independent Claim 278 words

A method for making an optical body having a distance viewing zone, a near viewing zone and an intermediate zone lying between boundaries with the distance and near zone, in which intermediate zone there is a gradual change in optical power along an eye path from the distance zone to the near zone, comprising the steps of: (a) selecting a rotationally symmetric base surface defined by a mathematical function which provides prescribed optical properties in the distance zone; (b) selecting a two dimensional coordinate system (u, v) in which, along the eye path, u equals a constant, and in which, along boundaries between the zones, v equals a constant; (c) defining a near zone add surface function, which, when summed with the base surface function, defines a surface approximating the prescribed optical properties in the near zone; (d) deriving a preliminary polynomial function in the coordinate system defining a surface for the intermediate zone such that the surfaces of the zones are the same height at the boundaries and such that at least the first three partial derivatives with respect to the surface functions in the three zones are the same at the boundaries; (e) adding the base surface function to the functions obtained in steps (c) and (d) in their respective zones to provide preliminary surface functions defining the surfaces of the near zones and intermediate zone, respectively; (f) evaluating the optical properties of the surface defined by the functions obtained in steps (a) and (e); (g) modifying the shape of the zone boundaries; (h) repeating steps (b) through (e) to obtain final surface functions; and (i) forming the optical body responsive to said final surface functions.

Claim 47

Dependent Claim 26 words

The method of claim 40 further comprising the step of: (j) using said optical body to profile a former for further formation of such optical bodies.

Claim 48

Independent Claim 173 words

A method for making a lens having a distance viewing zone, a near viewing zone and an intermediate zone lying between boundaries with the distance and near zones, in which intermediate zone, there is a gradual change in optical power along an eye path from the distance zone to the near zone, comprising the steps of (a) selecting a preliminary surface function, defined piece-wise as zero in the distance zone, a polynomial function in the intermediate zone and a quartic surface in the near zone; (b) selecting an auxiliary surface function continuous in all derivatives up to and including the third; (c) obtaining the product of the preliminary surface function and the auxiliary function; (d) evaluating the product obtained in step (c) for astigmatism and orthoscopy; (e) modifying the auxiliary function selected in step (b); (f) repeating steps (b) through (e) until a final product function is evaluated to have the desired astigmatism and orthoscopy characteristics in the intermediate and near zones; and (g) forming a lens responsive to the final product function.

Claim 49

Independent Claim 173 words

A method for making a lens having a distance viewing zone, a near viewing zone and an intermediate zone lying between boundaries with the distance and near zones, in which intermediate zone, there is a gradual change in optical power along an eye path from the distance zone to the near zone, comprising the steps of (a) selecting a preliminary surface function, defined piece-wise as zero in the distance zone, a polynomial function in the intermediate zone and a quartic surface in the near zone; (b) selecting an auxiliary surface function continuous in all derivatives up to and including the third; (c) obtaining the product of the preliminary surface function and the auxiliary function; (d) evaluating the product obtained in step (c) for astigmatism and orthoscopy; (e) modifying the auxiliary function selected in step (b); (f) repeating steps (b) through (e) until a final product function is evaluated to have the desired astigmatism and orthoscopy characteristics in the intermediate and near zones; and (g) forming a lens responsive to the final product function.

Claim 50

Dependent Claim 24 words

The method of claim 42 further comprising the step of: (h) using said lens to profile a former for further formation of such lenses.

Claim 51

Dependent Claim 54 words

The method of claim 42 wherein a factor S(y) of the auxiliary function is of the form: ##EQU15## where y is a cartesian coordinate, and where y c and σ y are constants, whereby the constants are selected to reduce astigmatism in a portion of the lens lying above the line y c =y.

Claim 52

Dependent Claim 72 words

The method of claim 42 wherein a factor U(u) of the auxiliary function is of the form: U(u)=e.sup.- (u/σ.sub.u).sup.4 for all u, where u is a coordinate of a curvilinear coordinate system in which the line u=o is the eye path, and where σ u is a constant, whereby the constant σ u is selected to improve orthoscopy in a portion of the intermediate zone on both sides of the eye path.

Annuity Stage	Window Opens	Payment Deadline	Surcharge Period Until	Estimated Fee	Status
3.5 Years (Year 4)	1990-06-29	1990-12-29	1991-06-30	$2000.00	Window Closed / Lapsed
7.5 Years (Year 8)	1994-06-29	1994-12-29	1995-06-30	$3760.00	Window Closed / Lapsed
11.5 Years (Year 12)	1998-06-29	1998-12-29	1999-06-30	$7700.00	Window Closed / Lapsed

Method of making progressive lens surface and resulting article

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