Lens for ophthalmic use for varying the depth of field

Abstract

Implantable or wearable lens for ophthalmic use, having a front surface and a rear surface, wherein at least one surface of said front surface and rear surface has a refractive profile of the multi-zone aspheric type with circular or rotational symmetry, with respect to the optical axis, and having a geometric elevation z(r) defined by a Forbes polynomial series expansion. This refractive profile enhances the wavefront W(r) emerging from the lens, progressively and continuously extending the depth of field in a range of powers preferably comprised between -1,0D and 4.0D; and improves the quality of vision in Far Field for pupil diameters greater than a value ϕ. Furthermore, the rear surface of the lens can include a toric-type profile adapted to correct residual corneal astigmatism.

Description

[0001] LENS FOR OPHTHALMIC USE FOR VARYING THE DEPTH OF FIELD

[0002] *************

[0003] Field of the invention

[0004] The present invention relates to an ophthalmic lens designed to be capable of adapting the depth of field. In particular, it is a lens that maintains optimal performance even when significant variations in depth of field are necessary, without compromising visual quality.

[0005] Background art

[0006] As is known, there are lenses for ophthalmic use which have at least one of the two aspherical surfaces defined by a single polynomial expansion of a series of powers of even order.

[0007] The purpose of these lenses is to vary the depth of field, manipulating the spherical aberration in the different zones of the optics defined as aspherical.

[0008] The surface of such lenses can be divided into concentric adjacent zones between which a discontinuity can exist and in which the aspherical surface is described through a single polynomial expansion expressed with a series of powers of even order.

[0009] Other technical solutions for ophthalmic lenses consist of a first front surface and a second rear surface, in which one of the two surfaces comprises a refractive profile while the other surface comprises a diffractive profile; in turn the refractive surface can be defined by a continuous aspherical profile of high order.

[0010] The technical solutions available suggest the use of an aspherical refractive surface defined by a polynomial in series of powers of even order up to high orders above the 4th order, at most up to the 6th order.

[0011] This type of technical solution does not allow manipulating the spherical aberration of orders greater than or equal to the sixth order so as to optimize the vision quality in the specific depth of field range. Aspherical surfaces are defined by a continuous aspherical profile of high order which describes the elevation of a given number of zones in a single equation. Given the numerical approximation attributable to the use of the polynomial in series of powers and given the number of said zones, defined in a manner unrelated to an optimization of the vision quality in the depth of field range considered, with the aspherical refractive lens expressed through the polynomial expansion of powers, it is not allowed to define a profile which allows manipulating the spherical aberration in a robust manner and expressing, in a manner less prone to errors, the number of zones and the elevation variations of the lens surface in said zones required to enhance the wavefront corresponding to the depth of field range to be reached.

[0012] The numerical approximation attributable to the use of the polynomial in power series of the aspherical surfaces can be highly inefficient and numerically unstable, i.e. , prone to rounding errors. The main reason for these limitations is the fact that the set of polynomials used to represent the aspherical surface (even order powers) is not orthogonal.

[0013] The number of lens zones described in the prior art and the elevation of said zones, if defined in a manner unrelated to an optimization of vision quality in the specific depth of field range, does not allow manipulating the spherical aberrations without compromising vision quality.

[0014] Some lenses are known with a number of zones correlated to an optimization of the vision quality in a specific depth of field range, which allow an adequate manipulation of the spherical aberrations. However, with some of these lenses, FAR field vision (zero diopters) is subject to reduced performance, particularly for pupillary diameters greater than about 2.7 mm, preferably greater than 3 mm, which can affect visual quality in low light conditions. On the other hand, with others of these lenses the vision in FAR Field is optimal but the vision in the NEAR Field is poor.

[0015] Therefore, there is a need to create an innovative lens which allows overcoming the aforesaid drawbacks found in lenses according to the prior art.

[0016] Summary of the invention

[0017] The object of the present invention is to provide an intraocular or wearable lens adapted to allow specific variations, even extended, of the depth of field without compromising the vision quality in the reference range, with an optimal vision in FAR Field, in particular for pupil diameters greater than about 2.7 mm, preferably greater than 3 mm, ensuring good visual quality even in low light conditions, while maintaining good image quality also in the INTERMEDIATE Field and NEAR Field. It is another object of the invention to provide a lens in which, for different pupil diameters, at least one surface of the lens is characterized by zones adapted to optimize the TFMTF (through focus modulation transfer function) in a desired range of vision and enhance the wavefront so as to make the extended variation of the depth of field possible without compromising vision quality. TFMTF is a transfer function which describes the vision quality through the lens optics. The meaning thereof will be shown in more detail in the following paragraphs.

[0018] Therefore, the present invention aims to achieve the objects discussed above by providing, according to a first aspect, an implantable or wearable corrective lens for ophthalmic use having a front surface and a rear surface, wherein the front surface or the rear surface comprises an aspheric refractive profile with circular or rotational symmetry with respect to the optical axis, wherein said aspheric refractive profile is divided into at least three concentric and coaxial zones (Z1 , Z2, Z3, ... Zn), the profile of each zone being of only refractive type and having a geometric elevation z(r) defined by a Forbes polynomial series expansion at least up to the third term where i = index of the polynomial, which is variable from 0 to x, where 2<x<11 , r = aperture radius of the at least one surface, which is variable from 0 to rmax, c = inverse of the radius of curvature R of the base sphere of said at least one surface, k = conical constant of said at least one surface, rmax = maximum aperture radius of said at least one surface

[0019] Qi= Jacobi polynomials of index (a=0 and (3=4) qi = coefficients of the Jacobi polynomials Qi, wherein the coefficients qi of the Jacobi polynomials to define the refractive profile of each coaxial zone all have a value equal to zero for the refractive profile of the outermost annular zone (Zn) and non-zero for the refractive profile of a central zone (Z1 ) and at least one intermediate annular zone (Z2, ... Zn-1); wherein the coefficients qi of the Jacobi polynomials to define the refractive profile of one or more intermediate annular zones, which only include pupillary diameters greater than a value comprised in a range from 2.7 mm to 3.0 mm, are comprised in respective ranges such that the value of the difference between the maximum value qimax and the minimum value qimin of each range, starting from the range of the coefficient q0of the first term up to the range of the coefficient qxof the last term of said Forbes polynomial series expansion, decreases exponentially according to a first function of the index of polynomial i with coefficient a comprised in a range from 0.0010 to 0.050, and coefficient b comprised in a range from -1.10 to -0.60; wherein said aspheric refractive profile is divided into six zones (Z1 , Z2, Z3, Z4, Z5, Z6), the profile of each zone having said geometric elevation z(r) defined by a Forbes polynomial series expansion up to the twelfth term, where the index of polynomial i varies from 0 to 11 ; wherein, starting from said optical axis, a fourth zone (Z4) and a fifth zone (Z5) of said six zones are the intermediate annular zones which exclusively include pupillary diameters greater than the value wherein the coefficients qi of the Jacobi polynomials to define the refractive profile of said fourth zone (Z4) are comprised in respective ranges such that the value of the difference between the maximum value qimax and the minimum value qimin of each range, starting from the range of the coefficient q0of the first term up to the range of the coefficient qn of the twelfth term, decreases exponentially according to said first function of the index of polynomial i with coefficient a comprised in a range from 0.030 to 0.050, preferably from 0.035 to 0.045, and coefficient b comprised in a range from -0.75 to -0.60, preferably from -0.70 to -0.60; wherein the coefficients qs of the Jacobi polynomials to define the refractive profile of said fifth zone (Z5) are comprised in respective ranges such that the value of the difference between the maximum value qjmax and the minimum value qimin of each range, starting from the range of the coefficient q0of the first term up to the range of the coefficient qn of the twelfth term, decreases exponentially according to said first function of the index of polynomial i f(i)=(qimax- qimin)=3 6^ ' with coefficient a comprised in a range from 0.0020 to 0.0030, and coefficient b comprised in a range from -1 .10 to -0.90, preferably from -1 .05 to -0.95; wherein the modulus of the OTF (optical transfer function module) has a maximum value greater than or equal to 0.35 at the far field, for a depth of field expressed in diopters equal to 0D, at 50 Ip / mm and for a pupil diameter greater than 3.0 mm; and wherein said modulus of the OTF always has a value greater than 0.1 for a depth of field in a range between 2D and 3D (near field), at 50 Ip / mm and for a pupil diameter less than 3.0 mm.

[0020] A further aspect of the present invention relates to a design method for an implantable or wearable corrective lens for ophthalmic use, with the purpose of producing the lens with a front surface and a rear surface, wherein the front surface or the rear surface comprises an aspheric refractive profile with circular or rotational symmetry with respect to the optical axis, wherein said aspheric refractive profile is divided into at least three concentric and coaxial zones (Z1 , Z2, Z3, ... Zn), the profile of each zone being of only refractive type and having a geometric elevation z(r) defined by a Forbes polynomial series expansion at least up to the third term where i = index of the polynomial, which is variable from 0 to x, where 2<x<11 , r = aperture radius of the at least one surface, which is variable from 0 to rmax, c = inverse of the radius of curvature R of the base sphere of said at least one surface, k = conical constant of said at least one surface, rmax = maximum aperture radius of said at least one surface

[0021] Qi= Jacobi polynomials of index (a=0 and (3=4) qi = coefficients of the Jacobi polynomials Qi, wherein the coefficients qi of the Jacobi polynomials to define the refractive profile of each coaxial zone all have a value equal to zero for the refractive profile of the outermost annular zone (Zn) and non-zero for the refractive profile of a central zone (Z1 ) and at least one intermediate annular zone (Z2, ... Zn-1); wherein the coefficients qi of the Jacobi polynomials to define the refractive profile of one or more intermediate annular zones, which exclusively include pupillary diameters greater than a value comprised in a range from 2.7 mm to 3.0 mm, are comprised in respective ranges such that the value of the difference between the maximum value qimax and the minimum value qimin of each range, starting from the range of the coefficient q0of the first term up to the range of the coefficient qxof the last term of said Forbes polynomial series expansion, decreases exponentially according to a first function of the index of polynomial i f(i)=qimax - qimin=a e*)' with coefficient a comprised in a range from 0.0010 to 0.050, and coefficient b comprised in a range from -1.10 to -0.60; wherein said aspheric refractive profile is divided into six zones (Z1 , Z2, Z3, Z4, Z5, Z6), the profile of each zone having said geometric elevation z(r) defined by a Forbes polynomial series expansion up to the twelfth term, where the index of polynomial i varies from 0 to 11 ; wherein, starting from said optical axis, a fourth zone (Z4) and a fifth zone (Z5) of said six zones are the intermediate annular zones which exclusively include pupillary diameters greater than the value wherein the coefficients qi of the Jacobi polynomials to define the refractive profile of said fourth zone (Z4) are comprised in respective ranges such that the value of the difference between the maximum value qimax and the minimum value qimin of each range, starting from the range of the coefficient q0of the first term up to the range of the coefficient qn of the twelfth term, decreases exponentially according to said first function of the index of polynomial i f(i)=qimax - qimin=a e*)' with coefficient a comprised in a range from 0.030 to 0.050, preferably from 0.035 to 0.045, and coefficient b comprised in a range from -0.75 to -0.60, preferably from -0.70 to -0.60 or -0.75 to -0.65; wherein the coefficients qi of the Jacobi polynomials to define the refractive profile of said fifth zone (Z5) are comprised in respective ranges such that the value of the difference between the maximum value qimax and the minimum value qimin of each range, starting from the range of the coefficient q0of the first term up to the range of the coefficient qn of the twelfth term, decreases exponentially according to said first function of the index of polynomial i f(i)=qimax - qimin=a e*)' with coefficient a comprised in a range from 0.0020 to 0.0030, and coefficient b comprised in a range from -1 .10 to -0.90, preferably from -1 .05 to -0.95; whereby the modulus of the OTF (optical transfer function module) has a maximum value greater than or equal to 0.35 at the far field, for a depth of field expressed in diopters equal to 0D, at 50 Ip / mm and for a pupil diameter greater than 3.0 mm; and whereby said modulus of the OTF always has a value greater than 0.1 for a depth of field in a range between 2D and 3D (near field), at 50 Ip / mm and for a pupil diameter less than 3.0 mm.

[0022] The lens of the present invention is intended to meet certain customer and market needs. In particular, the lens of the invention is a progressive multi-zone aspheric intraocular lens, with extended depth of focus, to be implanted in the capsular bag to replace the human crystalline lens and correct aphakia and presbyopia in adult patients.

[0023] A further aspect of the invention relates to an intraocular lens in which the one of the front surface and rear surface that does not have said aspheric refractive profile with circular symmetry comprises at least one toric portion, or is a toric surface.

[0024] Therefore, the correction of corneal astigmatism is obtained in the present ophthalmic lens by means of an at least partially toric surface applied on the side opposite to the side comprising the multi-zone aspherical surface. For example, if the multi-zone aspherical surface intended to extend the depth of field is on the front side (facing the cornea), the toric surface will be positioned on the rear side of the lens (facing the retina), or vice versa.

[0025] Therefore, a surface of this lens will have a toric shape with two different curvatures, one along the more curved main axis and the other along the less curved main axis. This means that the aforesaid surface will not be symmetrical with respect to the central axis thereof, like a spherical lens. Therefore, the asymmetry of the toric lens can be defined as cylindrical or non-rotational or elliptical symmetry, indicating the variation of the curvature and consequently of the optical power along two main directions.

[0026] In the case of a progressive toric aspheric lens, the lens therefore comprises an at least partially toric surface, specifically designed to compensate corneal astigmatism, and a further multi-zone aspherical surface which allows increasing the depth of field, whereby FAR Field vision is further improved for pupillary diameters greater than about 2.7 mm, preferably greater than 3 mm.

[0027] These progressive intraocular lenses, designed in an aspheric manner and preferably toric, are foldable, pre-loaded in a special injector and provided with a UV filter which ensures additional protection for the eye and an overall improvement of the patient's visual experience.

[0028] A further aspect of the invention further relates to a two-lens system such as that described above, said two lenses being complementary for an extension of the depth of field in binocular vision.

[0029] The aforesaid refractive profile generates an optimization of the TFMTF and an enhancement of the wavefront W(r) emerging from the lens, which yields a variation of the depth of field of the lens in a desired power range, preferably in a region of maximum amplitude between -1 ,0D and +4.0D (D = diopters), without compromising the vision quality, therefore with an additional power or residual power up to +4.0D. Preferably, only in an inner or central zone and in the intermediate annular zones of said coaxial zones there is provided (induced) a spherical aberration, preferably from the fourth order to the twenty-fourth order, and an optical power discontinuity is always provided between each coaxial zone and the next.

[0030] Considering a further aspect, the present invention aims to achieve the aforementioned objects by providing an implantable or wearable corrective lens for ophthalmic use, having a front surface and a rear surface, wherein at least one surface of said front surface and rear surface has a multi-zone aspheric refractive profile with circular or rotational symmetry with respect to the optical axis and divided into at least three coaxial zones, for example at least six zones, the profile of each zone being of refractive type only, wherein said coaxial zones consist of an inner or central zone (Zin) extending from the optical axis to a first outer radius nn, at least one intermediate annular zone (Zjnt) extending from said first outer radius On to a second outer radius Gnt, and an outer annular zone (Zout) extending from said second outer radius nntto a third outer radius rout, coinciding with the outer radius of the lens surface; wherein only in the central zone (Zin) and in the at least one intermediate annular zone (Zjnt) a spherical aberration is provided, or induced, preferably from the fourth order to the twenty-fourth order, while the outer annular zone (Zout) has an aspherical monofocal profile with optical power such as to correct or attenuate the positive spherical aberration induced by the cornea.

[0031] Preferably, the correction of corneal astigmatism is obtained by means of a toric surface applied on the side of the lens opposite to that comprising the multi-zone aspherical surface.

[0032] With reference to all the aspects of the invention, a particular lens variant provides said at least one surface provided with six concentric coaxial zones Z1 , Z2, Z3, Z4, Z5, Z6 with circular symmetry; wherein, as the radius increases, the total optical power of the first central zone Z1 starting from the center of the lens:

[0033] - decreases from a first value P1 to a second value P2 in the presence of a negative spherical aberration in a first central sub-zone;

[0034] - and increases from said second value P2 to a third value P3 at the first outer radius r1 in the presence of a positive spherical aberration in a second central sub-zone; preferably wherein the total optical power in the second intermediate annular zone Z2, starting from the first outer radius r1 , decreases from a fourth value P4 to a fifth value P5 in the presence of a negative spherical aberration in said second intermediate annular zone Z2; preferably wherein the fourth value P4 is less than the second value P2; preferably, wherein the total optical power in the third intermediate annular zone Z3 starting from the second outer radius r2:

[0035] - decreases from a sixth value P6 to a seventh value P7 in the presence of a negative spherical aberration in an initial part of said third intermediate annular zone Z3; - and increases from said seventh value P7 to an eighth value P8 at the third outer radius r3 in the presence of a positive spherical aberration in a final part of said third intermediate annular zone Z3, preferably wherein both the sixth value P6 and the seventh value P7 are comprised in the range comprised between the fourth value P4 and the fifth value P5, and wherein the eighth value P8 is greater than the third value P3 of the central zone Z1 ; preferably wherein the total optical power in the fourth intermediate annular zone Z4 starting from the third outer radius r3 increases from a ninth value P9 to a tenth value P10 at the fourth outer radius r4 in the presence of an overall positive spherical aberration in said fourth intermediate annular zone Z4; preferably wherein the total optical power in the fifth intermediate annular zone Z5 starting from the fourth outer radius r4 decreases from an eleventh value P11 to a twelfth value P12 at the fifth outer radius r5 in the presence of a negative spherical aberration; preferably wherein the average power value between P11 and P12 is substantially lower than the average power value in the fourth intermediate annular zone Z4; preferably wherein the total optical power in the sixth outer annular zone Z6 starting from the fifth outer radius r5 decreases from a thirteenth value P13 to a fourteenth value P14 at the outer radius r6 in the presence of a negative spherical aberration; preferably wherein the average power value between P13 and P14 is substantially slightly lower than or equal to the average power value in the fifth intermediate annular zone Z5.

[0036] In the description of the present invention, the following technical terms have the following respective definitions.

[0037] Depth of field

[0038] Depth of field means the distance separating the two extreme points which limit the front and back of the zone of the space where an object appears sharp and recognizable. This value can be expressed in units of length (meters or millimeters) or in diopters, by applying the known optical power formula P[D]=1000 / L[mm] to each of the two extreme points and calculating the difference of the values thus obtained.

[0039] Depth of focus means the range of focusing planes on which an image remains sharp in the plane of the retina. This is also a measure of de-focusing tolerance and is most often used especially in technical contexts such as photography and microscopy.

[0040] Through Focus Modulation Transfer Function (TFMTF)

[0041] The TFMTF function expresses the optical quality of an intraocular lens (IOL) on different focal planes and represents how the modulus of the optical transfer function (OTF) varies as a function of the position of an object target expressed in diopters. The ordinate axis (in any TFMTF graph reported in this document - for example the one of Fig. 8) represents the modulus of the OTF (i.e. , the MTF) as a function of the depth of field, i.e., the position of the object target, measured in diopters, situated in front of the patient's eye: at each point on the axis of the abscissa, the TFMTF graph shows how the quality of the image projected on the retina varies when the object target is moved, for example, from -0.5D to +4D diopters (i.e., from -2m, in this case the position of the target can be virtual and obtainable for example with the aid of lenses, up to 0.25m).

[0042] The vertical axis represents the modulus of the OTF (modulus of the optical transfer function), i.e., MTF, a value used to express the quality of the image formed by the lens. The MTF values are between 0 and 1 , where 0 indicates a very poor image quality, i.e., no spatial information is transferred, through the optical medium, from the object plane to the image plane, while 1 indicates a perfect image quality, i.e., all spatial information is transferred, through the optical medium, without losing quality from the object plane to the image plane.

[0043] In more detail, in some TFMTF graphs shown in this description (Figures 13-17) there are two curves representing the image quality for two different meridians or orthogonal directions referring to the human eye, which are the tangential meridian and the sagittal meridian, respectively.

[0044] In more detail:

[0045] Tangential meridian (dashed blue curve): refers to the MTF value calculated in the tangential plane, which is the plane defined by the axis of symmetry of the optical system in question (human eye) and a point of the field in the object space;

[0046] • Sagittal meridian (continuous blue curve): refers to the MTF value calculated in the plane orthogonal to the tangential plane, which also intersects the axis of symmetry at the position of the entrance pupil.

[0047] For example: for typical rotational symmetry systems with axis of symmetry Z and with field points lying along the axis Y, the tangential plane is the plane YZ while the sagittal plane is the plane orthogonal to the plane YZ that intersects the center of the entrance pupil.

[0048] The trend of these tangential and sagittal TFMTF functions shows how the quality of the image reproduced by the optical system in question (for example, the human eye in which the crystalline lens has been replaced by the IOL) changes as the depth of field varies; in particular, the highest points in the curves (peaks) indicate the positions where the target object has an optimal focusing quality, i.e., where the lens provides the highest quality of the image projected on the retina; the lowest points in the curves (minimums) indicate the points of worst image quality, due to a greater de-focusing.

[0049] For an EDOF (Extended Depth of Focus) lens, the curve trend is particularly significant.

[0050] The amplitude of the peaks indicates the ability of the lens to maintain good image quality over a wider range of focus displacements. Curves with higher and wider peaks therefore indicate a lens with a better depth of focus.

[0051] The similar trend between the TFMTF functions for two different meridians or orthogonal directions referring to the human eye, which are the tangential meridian and the sagittal meridian, respectively, indicates a good balance of power between the two meridians and demonstrates that the lens maintains a homogeneous image quality in all directions, an important condition for sharp vision at different distances in the presence of a corneal toric deformation.

[0052] Geometric elevation

[0053] Geometric elevation z(r) means the sagittal height of a surface, which is the vertical distance between the surface and a base line or a reference plane in a specific point r with respect to the axis of symmetry of the surface itself. The lens of the invention has a refractive optical design with circular symmetry on at least one of the two surfaces which enhances the emerging wavefront so as to extensively vary the depth of field.

[0054] The wavefront enhancement contribution is such as to correspond to a desired range of vision extension, expressed through a target function Target(d, y) which describes the Through Focus Modulation Transfer Function (TFMTF) as a function of a predetermined pupil diameter d and a determined focusing position on the retina y expressed in mm, or as a function of a predetermined pupil diameter d and a depth of field expressed in diopters.

[0055] At least one surface of the lens of the invention, front or rear, is divided into at least three concentric and coaxial zones, preferably six zones, the aspherical profile of which is obtained by separately describing the aspherical profile of each ring or zone by a Forbes polynomial series. Said zones are annular except for the central or innermost portion of the lens surface. Advantageously, the lens of the present invention allows the depth of field to be extended by dividing the (front or rear) surface into at least three concentric annular zones of refractive-only type.

[0056] The division into annular portions is such as not to require the introduction of a thickness discontinuity in the junction or transition zone between two adjacent zones or portions, thereby reducing the risk of occurrence of vision side effects (halos and glare).

[0057] Each zone of the lens surface is not simply configured to extend the depth of field at a well-defined distance from the patient's eye, but to extend it in a more or less wide region of distances from the patient: in fact, each zone partially and separately contributes to improving vision in both the near field and the far field.

[0058] The profile of each surface ring or zone is obtained by a Forbes polynomial series. Forbes polynomials are advantageous for defining aspherical surfaces with respect to the classic polynomial expansion (with a series of powers of even order) since they have units of length and therefore the value thereof also represents the contribution thereof to surface variation, for example, in mm. Furthermore, unlike the series of powers where the coefficients are statistically insignificant if establishing a tolerance on the coefficient itself is sought, the Forbes polynomial coefficients can be assigned tolerances which are significant for the design and construction of the aspherical surface. Applied to define the surface, the Forbes series minimizes the difference between the real TFMTF(D, y), obtained by simulating the behavior of the lens of the invention within an optical model of the human eye, and a reference TFMTF function known as Target(D, y) and which describes the desired extension of the depth of field, simultaneously evaluating the extension for different pupil diameters, for example, between di = 2.0 mm and d2 = 4.5 mm.

[0059] Such a Forbes series has been introduced in order to provide a more robust representation of the aspherical surfaces of individual lens optics zones.

[0060] The aspherical surface described, in the prior art, through a polynomial in traditional series of powers is broken down into two parts: a base component (conical section) and a series of powers of even order which takes into account the deviations of the surface from the conical base, according to the following formula: where c = 1 / R, the curvature of the surface, and k, the conical constant, define the conical section.

[0061] The approximation of such a generic aspherical surface S(r)is obtained by a numerical procedure known as the least squares method.

[0062] It is known that the numerical stability of this solution strongly depends on the choice of polynomials {P . However, having found that the stability of the solution improves if we choose the polynomials {P so that they are orthogonal to each other, the inventors have discarded the use, provided in the prior art, of the polynomials in series of powers {P since they are not orthogonal to one another.

[0063] Forbes represents aspherical surfaces by introducing an alternative formula: in which, beyond the conical base section, a term appears given by the sum of polynomials {Q of a different nature with respect to the polynomials {P . Also in the case of Forbes, the optimal coefficients {q are chosen to approximate a generic aspherical surface z(r), minimizing a quadratic functional, where the polynomials {Q , which satisfy the orthogonality condition, correspond to Jacobi polynomials of index (a=0 and (3=4), i.e., correspond to a scaled version of the classic Jacobi polynomials, Ji(ct P)(r), with a=0 and [3=4, that is: Qi(r) = Ji(0’4)(2r-1 ), where r is the opening radius of the at least one surface.

[0064] The enhancement of the wavefront AW(r), capable of introducing a variation of the depth of field of the lens, is proportional to the sum of the orthogonal polynomials multiplied by the coefficients thereof.

[0065] In the context of the present invention, the coefficients qi are determined so as to minimize a merit function (M) defined by the difference between the Through Focus Modulation Transfer Function TFMTF(d, y) (for example at 50 Ip / mm and for an arbitrary number of predetermined pupil diameters - for example 2.0 mm, 3.0 mm, 4.5 mm, etc.) of the human eye model in which the lens of the invention is inserted, or on which it is worn, and a target Through Focus Modulation Transfer Function, called Target(d, y), which, at the same spatial frequency as TFMTF(d, y) and for the same pupil diameters, expresses the desired depth of field extension.

[0066] Examples of the target function, Target(d, y), are visible, for example, in Figures 5 and 6 where the TFMTF Target is depicted in green for a spatial frequency of 50lp / mm and a pupillary diameter of 2.0 mm (Figure 5) and for a spatial frequency of 50lp / mm and a pupillary diameter of 3.0 mm (Figure 6), respectively; the TFMTF obtained at the end of the optimization of the IOL lenses is depicted in blue.

[0067] The depth of field variation range, in which the minimization of the merit function M can tend to the absolute minimum thereof, can for example be between -0.5D and 4.0D.

[0068] The merit function M is defined by the following equation:

[0069] M = (TFMTF(d,y) - Targettd.y )2Eq. 2 where

[0070] TFMTF(d, y) = Through Focus Modulation Transfer Function of the lens;

[0071] Target(d, y) = target Through Focus Modulation Transfer Function; y = focus shift position on the retina (Focus Shift) in mm or depth of field in diopters (Depth of Field), d = pupil diameter in mm.

[0072] The enhanced wavefront in a given depth of field range has a specific shape thereof referring to a fixed pupillary diameter as depicted for example in Figure 1 , and which in general can also be discontinuous.

[0073] The replacement of the wavefront enhancement AW(r) within the merit function M (Equation 2) and the resulting numerical minimization lead to a series of coefficients qi which define the TFMTF(d, y) depicted in the graph in Figure 2, for example referring to a spatial frequency of 50 Ip / mm and a pupil diameter of 3.0 mm, which closely approximates the function Target(d, y). More in detail, in the overall wavefront associated with the function TFMTF(d, y) depicted in the graph in Figure 1 , the axis of the abscissa represents the normalized coordinate corresponding to the pupillary radius and the axis of the ordinates represents the corresponding variation value of the wavefront expressed in pm. This specific wavefront corresponds to a profile of a surface (e.g., the front surface) of an intraocular or wearable lens. Finally, the power distribution associated with the profile of the lens, referring to the pupil diameter, can be obtained from the expression of the wavefront as follows (see Eq. 5 below).

[0074] The dependent claims describe further possible embodiments of the invention. Brief description of the drawinqs

[0075] Further features and advantages of the present invention will become more apparent in light of the detailed description of non-exclusive embodiments of a lens disclosed by way of non-limiting example, with the aid of the accompanying drawings, in which:

[0076] Figure 1 depicts an enhanced wavefront in a given depth of field range;

[0077] Figure 2 depicts the Through Focus Modulation Transfer Function (TFMTF) at 50 Ip / mm and a pupil diameter of 3.0 mm as a function of the focus shift position y on the retina expressed in mm;

[0078] Figure 3 depicts the geometric elevation of the surface of an intraocular lens for depth of field variation (red color - curve 1 ) according to the invention, the geometric elevation of the surface of the same intraocular lens which does not apply the extended depth of field variation (blue color - curve 2), and the geometric elevation difference (green color - curve 3);

[0079] Figure 4A depicts the variation in power or residual power (in diopters) as a function of the radius of a lens extending for example from 0 to 1 .5 mm;

[0080] Figure 4B depicts the trend of the total power (in diopters) as a function of the radius of a lens extending from 0 to 3 mm and where the spherical base power of the lens is for example equal to +20D;

[0081] Figure 5 depicts a TFMTF for a lens with an extended depth of field, with a spatial frequency of 50lp / mm and referring to a pupil diameter of 2 mm;

[0082] Figure 6 depicts a TFMTF for a lens with an extended depth of field, with a spatial frequency of 50lp / mm and referring to a pupil diameter of 3 mm;

[0083] Figure 7 depicts an enhanced wavefront in the range from -0.25D to 3.5D;

[0084] Figure 8 depicts the Through Focus Modulation Transfer Function TFMTF at 50lp / mm and a pupil diameter of 3.0 mm as a function of the depth of field in the range between -0.5D and 4.0D of a multi-zone aspheric lens according to the invention;

[0085] Figure 9 depicts an example of a lens of the invention with six zones in which a multi-zone aspherical surface is divided;

[0086] Figure 10a depicts the trend of the total optical power of said lens as a function of the radius;

[0087] Figure 10b depicts the trend of the tangential and sagittal total optical power of said lens as a function of the radius;

[0088] Figure 10c depicts the graph of Figure 10a divided into six zones, comprised between 0 mm and 3 mm of pupil radius;

[0089] Figures 10d-10i depict the trend of the total optical power of said lens in the respective six zones;

[0090] Figure 10j depicts the trend of the total optical power of said lens in the three outermost zones, preferably comprised between a pupil radius of 1.37 mm and 3.0 mm;

[0091] Figure 11a graphically depicts the maximum and minimum values for each of the Jacobi coefficients related to the annular zone Z4; Figure 11 b graphically depicts the maximum and minimum values for each of the Jacobi coefficients related to the annular zone Z5;

[0092] Figure 11 c graphically depicts the maximum and minimum values for each of the Jacobi coefficients related to the central zone Z1 ;

[0093] Figure 11d graphically depicts the maximum and minimum values for each of the Jacobi coefficients related to the annular zone Z2;

[0094] Figure 11e graphically depicts the maximum and minimum values for each of the Jacobi coefficients related to the annular zone Z3;

[0095] Figure 12a depicts the trend of the value of the difference between the maximum and minimum values for each of the Jacobi coefficients, referring respectively to the annular zone Z4 (continuous curve) and to the annular zone Z5 (dashed curve);

[0096] Figure 12b depicts the trend of the value of the difference between the maximum and minimum values of the individual Jacobi coefficients corresponding to the annular zone Z4;

[0097] Figure 12c represents the trend of the value of the difference between the maximum and minimum values of the individual Jacobi coefficients corresponding to the annular zone Z5;

[0098] Figures 13 to 18 depict the Through Focus Modulation Transfer Function TFMTF for the tangential meridian (continuous curve) and the sagittal meridian (dashed curve) at 50lp / mm and for a pupil diameter of 2.0 mm, 2.5 mm, 3.0 mm, 3.5 mm, 4.0 mm and 5.0 mm respectively as a function of the depth of field in the range between -1.0D and 4.0D of a multi-zone aspheric lens according to the invention.

[0099] The same reference numerals in the figures identify the same elements or components.

[0100] Detailed description of preferred embodiments of the invention

[0101] The lens of the invention has a refractive optical design with circular or rotational symmetry with respect to the optical axis on at least one of the two surfaces, front and rear surfaces, and enhances the emerging wavefront W(r) so as to extend the depth of field of the lens itself.

[0102] Advantageously, the optical design of the lens of the invention which enhances the wavefront W(r) is represented by the geometric elevation z(r) of at least three coaxial zones, with an aspherical refractive profile, having circular symmetry with respect to the optical axis, of at least one surface of the front surface and the rear surface of the lens. Circular or rotational symmetry means that this surface of the spherical lens has the same curvature in all directions referring to the center thereof. This means that this lens surface is symmetrical with respect to the central axis thereof and has the same optical power regardless of the angle of incidence of the light.

[0103] Said geometric elevation z(r), or sagittal height, of the coaxial zones is defined through a respective expansion in Forbes polynomials at least up to the third term (Eq. 3): where i = index variable from 0 to x, where 2<x<11 , r = opening radius of at least one of the two lens surfaces, which is variable from 0 to Tmax, c = curvature of the base sphere of said at least one of the two surfaces, k = conical constant of said at least one of the two surfaces, rmax = maximum opening radius of said at least one of the two surfaces,

[0104] Qi = Jacobi polynomials of index (a=0, (3=4) qi = coefficients of the Jacobi polynomials Qi.

[0105] Each variation of the coefficients qi directly corresponds to a variation of the geometric elevation of the lens surface. For example, appropriately modifying the geometric elevation of the surface (e.g., front surface) of an intraocular lens, a positive and / or negative power variation is induced as a function of the radius, i.e. , such as to distance (beyond the retina, if negative) or approach (before the retina, if positive) the focusing point (i.e., the energy distribution).

[0106] The elevation of said surface (e.g., front surface) of an intraocular lens for the depth of field variation is represented by curve 1 in Figure 3. The curve 2, shown in the same Figure 3, represents the trend of the geometric elevation of the surface (e.g., front surface) of the same intraocular lens which does not apply the extended depth of field variation. The difference between the aforesaid geometric elevations, highlighted by curve 3, although slight, is not negligible and involves a wavefront variation expressed in first approximation by Equation 4 (Eq. 4)

[0107] AW = (ni-n2) Az Eq. 4 where

[0108] AW = wavefront variation; ni = refractive index of the aqueous humor; n2 = refractive index of the lens material;

[0109] Az = geometric elevation difference of the surface of the lens of the invention.

[0110] This variation of the wavefront in turn causes a variation of power, which we will call residual power, which in general can also vary with discontinuity, and which is defined by the following equation (Eq. 5):

[0111] In the example shown, such a trend is shown in the graph of Figure 4A in which the variation in power or residual power (in diopters) is represented as a function of the radius of a lens, which extends for example from a pupil radius of 0.8 mm to a pupil radius of 1 .3 mm.

[0112] It can be seen from the graph in Figure 4A that the geometric elevation variation induces a power variation, slightly negative (lower than 0D) up to about 1.1 mm radius and positive (greater than 0D) between 1.1 mm and 1.3 mm radius. This variation in power, or residual power, therefore entails, with respect to the base power, a redistribution of energy towards the far field within 1.1 mm radius and towards the near field between 1.1 mm and 1.3 mm radius, increasing the vision quality (or depth of field) in the respective distances.

[0113] Therefore, the total power is defined by the sum of the base power and the residual power or additional power.

[0114] The graph in Figure 4B instead shows the trend of the total power (in diopters) as a function of the radius of a lens in a more complex case in which the intraocular lens radius extends, for example, from 0 to 3 mm and where the base power of the lens is equal to +20D. It is noted that in general, power variations characterized by the presence of peaks at some radii can emerge. The front (or rear) surface of the lens can be divided into a multiplicity of concentric zones delimited by progressive radii and variable with respect to the center of the lens, obtained in response to an optimization of the TFMTF. In each of these zones, the lens assumes a power, or a multiplicity of different powers, also obtained in response to an optimization of the TFMTF with the aim of bringing it as close as possible to an ideal reference TFMTF (Target TFMTF).

[0115] Some embodiments of the lens of the invention are shown below.

[0116] In all the embodiments thereof, the implantable or wearable corrective lens has a front surface and a rear surface.

[0117] At least one surface of said front surface and rear surface has an aspheric refractive profile with circular or rotational symmetry with respect to the optical axis and divided into at least three concentric and coaxial zones Z1 , Z2, Z3,... Zn, the profile of each zone being only refractive and having a geometric elevation z(r) defined by a Forbes polynomial series expansion at least up to the third term where i is the index of the polynomial, which is variable from 0 to x, where 2<x<11 . The coefficients qi of the Jacobi polynomials to define the refractive profile of each coaxial zone all have a value equal to zero for the refractive profile of the outermost annular zone Zn and non-zero for the refractive profile of a central zone Z1 and at least one intermediate annular zone Z2, ... Zn-1 .

[0118] Advantageously, the coefficients qi of the Jacobi polynomials to define the refractive profile of one or more intermediate annular zones, which exclusively include pupillary diameters greater than a value comprised in a range from 2.7 mm to 3.0 mm, are comprised in respective ranges such that the value of the difference between the maximum value qimax and the minimum value qimin of each range, starting from the range of the coefficient q0of the first term up to the range of the coefficient qxof the last term of said Forbes polynomial series expansion, decreases exponentially according to a first function of the index of polynomial i with coefficient a comprised in a range from 0.0010 to 0.050, and coefficient b comprised in a range from -1.10 to -0.60.

[0119] For example, said value can be equal to about 2.7 mm, or preferably equal to about 3.0 mm.

[0120] The above-described configuration of the intermediate annular zones, which include a pupil diameter greater than the value (|), advantageously induces better visual acuity in the FAR Field, only slightly reducing the performance in the NEAR Field for pupil diameters greater than the value (|), ensuring acceptable visual quality even in low light conditions.

[0121] Preferably, the coefficients qi of the Jacobi polynomials to define the refractive profile of, respectively, the central zone Z1 and of one or more possible intermediate annular zones, which include pupillary diameters less than or equal to said value (|), are comprised in respective ranges such that both the maximum values qimax and the minimum values qimin have a respective sinusoidal trend modulated by an exponentially decaying amplitude.

[0122] Said sinusoidal trend can be described by a second function of the index of polynomial i with coefficient A comprised in a range from 0.0032 to 0.12, coefficient b comprised in a range from 0.20 to 1.35, the coefficient C comprised in a range from 0.20 to 3.25, the coefficient D comprised in a range from -0.070 to 0.070, the coefficient E comprised in a range from -0.105 to 0.050, and the coefficient F comprised in a range from -0.002 to 0.002.

[0123] Advantageously, in a preferred variant of the lens of the invention, at least one surface of said front surface and rear surface has a multi-zone aspheric refractive profile with circular or rotational symmetry with respect to the optical axis and divided into six concentric and coaxial zones Z1 , Z2, Z3, Z4, Z5, Z6, the profile of each zone being only refractive and having a geometric elevation z(r) defined by a Forbes polynomial series expansion up to the twelfth term (Eq. 3) where i = index of the polynomial, which is variable from 0 to x=11 , r = aperture radius of the at least one surface, which is variable from 0 to rmax, c = curvature of the base sphere of said at least one surface, k = conical constant of said at least one surface, rmax = maximum opening radius of said at least one surface,

[0124] Qi = Jacobi polynomials of index (a=0, (3=4), qi = coefficients of the Jacobi polynomials Qi, where the Jacobi polynomials Qi of index (a=0 and [3=4) correspond to a scaled version of the classic Jacobi polynomials, Jj(a (3)(r), with a=0 and [3=4, i.e.: Qi(r) = J j(0 4)(2r-1 ), where r is the opening radius of the at least one surface.

[0125] The value of all the coefficients qi is non-zero for the refractive profile of the first five zones Z1 , Z2, Z3, Z4, Z5, in particular the central zone Z1 and the intermediate zones Z2, Z3, Z4, Z5, and is equal to zero for the refractive profile of the outermost zone Z6.

[0126] Starting from the optical axis, the fourth zone Z4 and the fifth zone Z5 are the intermediate annular zones which only include pupil diameters greater than the value (|), for example diameters greater than 2.7 mm, preferably greater than 3 mm. Advantageously, the coefficients qs of the Jacobi polynomials to define the refractive profile of the fourth zone Z4 are comprised in respective ranges such that the value of the difference between the maximum value qimax and the minimum value qimin of each range, starting from the range of the coefficient q0of the first term up to the range of the coefficient qn of the twelfth term, decreases exponentially according to a first function of the index i of the polynomial, shown in Figures 12a (continuous curve) and 12b, qimax - qimin=3 6^ ' with coefficient a comprised in a range from 0.030 to 0.050, preferably from 0.035 to 0.045, and coefficient b comprised in a range from -0.80 to -0.60, preferably from -0.75 to -0.65, or from -0.75 to -060, preferably from -0.70 to -0.60, even more preferably from -0.70 to -0.65. A preferred combination for the fourth zone Z4 provides the coefficient a comprised in a range from 0.030 to 0.050 and the coefficient b comprised in a range from -0.75 to -060, preferably from -0.70 to -0.60 or from -0.75 to -0.65.

[0127] Furthermore, the coefficients qi of the Jacobi polynomials to define the refractive profile of the fifth zone Z5 are comprised in respective ranges such that the value of the difference between the maximum value qimax and the minimum value qimin of each range, starting from the range of the coefficient q0of the first term up to the range of the coefficient qn twelfth term, decreases exponentially according to said first function of the index i of the polynomial, shown in Figures 12a (dashed curve) and 12c, qimax “ qimin=3 6^ ' with coefficient a comprised in a range from 0.0010 to 0.0040, preferably from 0.0020 to 0.0030, and coefficient b comprised in a range from -1.10 to -0.90, preferably from -1 .05 to -0.95.

[0128] A preferred combination for the fifth zone Z5 provides the coefficient a comprised in a range from 0.0020 to 0.0030 and coefficient b comprised in a range from -1 .10 to -0.90.

[0129] Figure 11a graphically depicts the maximum and minimum values for each of the Jacobi coefficients related to the annular zone Z4; while Figure 11 b graphically depicts the maximum and minimum values for each of the Jacobi coefficients related to the annular zone Z5. It is observed how the range between the maximum value qimax and the minimum value qimin, for each index i, is concentrated very close to the origin (axis of the abscissa) and tends to assume, as i increases from 0 to 11 , values closer to zero.

[0130] Figures 12a-c depict the trend of the value of the difference between the maximum and minimum values for each of the Jacobi coefficients, referring respectively to the annular zone Z4 (continuous curve) and to the annular zone Z5 (dashed curve).

[0131] As already clear from Figures 11a-b, in Figure 12a, it is observed how the value of the difference between the maximum and minimum values for each of the Jacobi coefficients is greater for the annular zone Z4 with respect to the annular zone Z5.

[0132] For example, in the fourth zone Z4, the value of the difference between the maximum value qimax and the minimum value qimin of each range decreases exponentially from 0.045 to 0.0003; while in the fifth zone Z5, the value of the difference between the maximum value qimax and the minimum value qimin of each range decreases exponentially from 0.0025 to 0.0000090.

[0133] The above-described configuration of the fourth zone Z4 and of the fifth zone Z5 advantageously induces better visual acuity in the FAR Field, however slightly reducing the performance in the NEAR Field for pupil diameters greater than about 2.7 mm, preferably greater than 3.0 mm, however ensuring good visual quality even in low light conditions.

[0134] Figures 13 to 18 depict the Through Focus Modulation Transfer Function TFMTF for the tangential meridian (continuous curve) and the sagittal meridian (dashed curve) at 50lp / mm and for a pupil diameter of 2.0 mm, 2.5 mm, 3.0 mm, 3.5 mm, 4.0 mm and 5.0 mm, respectively, as a function of the depth of field in the range between -1.0D and 4.0D of a multi-zone aspheric lens according to the invention, with spherical base power equal to 20D and cylindrical base power equal to 3D.

[0135] It should be noted that the FAR peak, substantially centered on the origin, is considerably higher for pupil diameters greater than 3 mm.

[0136] Advantageously, the modulus of the OTF (modulus of the optical transfer function), or MTF, has a maximum value greater than or equal to 0.35 at the far field, for a depth of field expressed in diopters equal to 0D, at 50 Ip / mm and for a pupil diameter greater than 3.0 mm, preferably greater than or equal to 3.5 mm.

[0137] In particular, for the pupil diameter of 3.5 mm or 4 mm, we observe that the peak of the FAR field reaches a value greater than or equal to 0.35, preferably comprised between 0.35 and 0.40. This increase in FAR peak entails a slight decrease in performance in the INTERMEDIATE vision region for depth of field around 1.5D.

[0138] Instead, for the pupil diameter of 5 mm, we observe that the FAR field peak reaches or slightly exceeds a value of about 0.40, preferably between 0.40 and 0.50. This increase in FAR peak entails a decrease in performance in the INTERMEDIATE vision region for depth of field around 1 .3D.

[0139] A further advantage is represented by the fact that said modulus of the OTF, or MTF, always has a value greater than 0.1 for a depth of field in a range between 2D and 3D (NEAR field), at 50 Ip / mm and for a pupil diameter less than 3.0 mm. This means that the lens of the invention induces good visual acuity in the NEAR Field even for pupillary diameters less than 3.0 mm.

[0140] Preferably, said modulus of the OTF, or MTF, always has a value greater than 0.15 for a depth of field in a range between 2D and 3D (NEAR field), at 50 Ip / mm and for a pupil diameter less than or equal to 2.5 mm.

[0141] Preferably, said modulus of the OTF, or MTF, always has a value greater than 0.20 for a depth of field in a range between 2D and 3D (NEAR field), at 50 Ip / mm and for a pupillary diameter less than or equal to 2.0 mm.

[0142] The modulus of the optical transfer function (OTF), commonly indicated as Modulation Transfer Function (MTF), is measured at the reference spatial frequency, for example 50 Ip / mm, and normalized to the unit value for the zero frequency. The measurement is based on the acquisition of the image generated by an object point (PSF) or by extended objects, as for example in the case of the edge spread function (ESF), followed by the application of the discrete Fourier transform of the resulting image.

[0143] In a first step, the MTFs are obtained through optical CAD simulations, using a model of the eye known in literature, Arizona model, in which the crystalline lens is replaced by the IOL of the invention, evaluating the performance for different pupil diameters and positions of the target object.

[0144] Subsequently, for experimental verification purposes, physical measurements are carried out on an optical model of the human eye. In such a configuration, the cornea is made by a plastic or glass lens, while the IOL is positioned inside a wet chamber filled with a saline solution similar to aqueous humor. An adjustable diaphragm placed in front of the IOL allows setting the desired pupil diameter in accordance with the test conditions provided for by ISO 11979-2.

[0145] The measurements can be performed using monochromatic light at A = 550 nm, so as to reduce the effects of chromatic dispersion and ensure the reproducibility of the results.

[0146] Preferably, the coefficients qi of the Jacobi polynomials to define the refractive profile of the central zone or first zone Z1 and of a second zone Z2 and third zone Z3, respectively, which are the zones including pupil diameters lower than or equal to value are comprised in respective ranges such that both the maximum values qimax and the minimum values qimin have a respective sinusoidal trend modulated by an amplitude which exponentially decays, as illustrated in Figures 11 c, 11 d and 11 e, respectively.

[0147] In a simplified variant, for the first zone Z1 said trend is described by said second function of the index of polynomial i with the coefficient Ai comprised in a range from 0.0032 to 0.0040, the coefficient Bi comprised in a range from 1.25 to 1.35, the coefficient Ci comprised in a range from 0.20 to 0.60, the coefficient Di comprised in a range from 0.005 to 0.070, the coefficient Ei comprised in a range from -0.105 to 0.005, and the coefficient Fi comprised in a range from -0.002 to 0.002; for the second zone Z2 said trend is described by said second function of the index of polynomial i with coefficient A2comprised in a range from 0.0075 to 0.0175, coefficient B2comprised in a range from 0.20 to 1.10, coefficient C2comprised in a range from 0.70 to 3.25, coefficient D2comprised in a range from -0.070 to -0.010, coefficient E2comprised in a range from -0.010 to 0.050; and coefficient F2comprised in a range from -0.002 to 0.002; and for the third zone Z3 said trend is described by said second function of the index of polynomial i with coefficient A3 comprised in a range from 0.08 to 0.12, coefficient B3 comprised in a range from 0.35 to 0.52, coefficient C3 comprised in a range from 1 .00 to 1 .30, coefficient D3 comprised in a range from -0.015 to 0.005, the coefficient E3 comprised in a range from 0.010 to 0.025, and the coefficient F3 comprised in a range from -0.002 to 0.002. Substantially, the behavior of the coefficients in zones Z1 , Z2 and Z3 fluctuates as a function of the index i, while the overall variation between the minimum and maximum values assumed by each index is very limited.

[0148] Preferably, a preferred lens variant provides a first lens surface, for example the front surface, described by an aspheric extension of the type described above, while on the second surface, in this case the rear one, a toric deformation is applied in order to correct the residual astigmatism of the patient's eye.

[0149] Therefore, the front surface has the aforesaid aspheric refractive profile with circular or rotational symmetry with respect to the optical axis, while the rear surface comprises at least one toric portion or consists of a toric surface; or vice versa.

[0150] Preferably, the spherical base power of the lens can vary in a range from 7.0D to 32.0D, optionally in steps of 0.5D, while the cylindrical base power can vary in a range from 1 ,0D to 5.0D, optionally in steps of 0.5D.

[0151] Preferably, the additional power or residual power of the lens can extend up to +4.0D.

[0152] A further advantage of this toric aspherical lens variant is that the extended depth of field makes the lens more tolerant to both defocusing and positioning inaccuracies (main meridian of the toric surface not perfectly aligned with the corneal meridian - i.e., rotation around the lens axis) making the lens more tolerant also to residual astigmatism.

[0153] The coefficients (q01... qi 1 ) vary as a function of the total power of the lens.

[0154] Preferably, the coefficients (q01... qn) of the Jacobi polynomials to define the refractive profile of each coaxial zone are comprised in the range -0.07< qi <0.11 .

[0155] In particular, the coefficients qi of the Jacobi polynomials to define the refractive profile of the first zone Z1 starting from said optical axis are in the following range - 0.001 < qi <0.004; the coefficients qs of the Jacobi polynomials to define the refractive profile of the second zone Z2 starting from said optical axis are in the following range -0.009< qi <0.015; the coefficients qs of the Jacobi polynomials to define the refractive profile of the third zone Z3 starting from the optical axis are in the following range - 0.069 <qi <0.108; the coefficients qi of the Jacobi polynomials to define the refractive profile of the fourth zone Z4 starting from said optical axis are in the following range -0.028 < qi <0.015; and the coefficients qi of the Jacobi polynomials to define the refractive profile of the fifth zone Z5 starting from said optical axis are in the following range -0.018< qi <0.005.

[0156] The refractive profile, described above, generates an enhancement of the wavefront W(r) emerging from the lens which translates into a depth of field variation of the lens in a power range which can at most expand in a range of values between -1 ,0D and 4.0D, preferably between -0.25D and 3.5D.

[0157] Preferably a spherical aberration is provided (induced) only in an inner or central zone and in the intermediate annular zones of said coaxial zones, said spherical aberration being preferably of an order higher than the fourth, and an optical power discontinuity is always provided between each coaxial zone and the next. However, no spherical aberration of any order is introduced in the outermost zone.

[0158] Advantageously, said at least one surface of said front surface or rear surface comprises at least six zones coaxial with each other and the axis of which coincides with the axis of the pupil, each zone being described by the respective twelve terms of the Forbes series expansion. These coaxial zones, except the central zone, are annular zones. Advantageously, said coaxial zones are adjacent to each other and a thickness continuity is provided in the junction or transition zone between two adjacent zones.

[0159] In each of the embodiments of the invention, all the aforesaid coaxial zones, i.e. , the inner or central zone, the intermediate annular zones and the outer annular zone can completely fill the aperture ("clear aperture") of the optics or lens. In a variant, the lens of the invention has an aspherical refractive optical design with circular symmetry with respect to the optical axis on one of the two surfaces, which enhances the emerging wavefront W(r) so as to extensively vary the depth of field in a power range between -0.25D and 3.5D. In particular, the refractive profile of the front or rear surface of the lens generates the wavefront enhancement. The enhanced wavefront in this specific depth of field range has a specific shape thereof as depicted in Figure 7. In such a depth of field range, the energy distributed from the enhanced wavefront is described, as shown for example in Figure 8, by the Through Focus Modulation Transfer Function TFMTF(d, y) for a pupil diameter of d=3.0 mm and a frequency of 50lp / mm. In this variant, at least one surface of the front surface and the rear surface consists of six concentric coaxial zones Z1 , Z2, Z3, Z4, Z5, Z6 adjacent to one another and each delimited by a respective maximum radius or outer radius r1 , r2, r3, r4, r5, r6, in which the coefficients q0, ... qn of the Jacobi polynomials to define the refractive profile of each coaxial zone (with the exception of zone Z6), through a Forbes polynomial expansion up to the twelfth term, are comprised in the following range -0.07 < qj < 0.11 with i = 0, ... 11.

[0160] In particular, the coefficients q0,... qn can be comprised in the following ranges, respectively:

[0161] In all the embodiments of the lens of the invention the maximum radii or outer radii of each zone are between 0.5 mm and 3 mm.

[0162] The lens is made of hydrophilic-hydrophobic acrylic material, preferably a hydrogel copolymer of 2-hydroxyethyl methacrylate (2-HEMA) and 2-ethoxyethyl methacrylate (EOEMA) with a water content of 20-30%, for example 25%, including a hydroxyphenyl triazine (HPT)-based UV absorber.

[0163] EXAMPLE

[0164] In this example of the lens of the invention, the front surface or the rear surface of the lens has six coaxial zones Z1 , Z2, Z3, Z4, Z5, Z6 adjacent to one another and each delimited by a respective maximum radius or external radius r1 , r2, r3, r4, r5, r6, and the coefficients q0,... qn of the Jacobi polynomials to define the refractive profile of each coaxial zone Z1 , Z2, Z3, Z4, Z5, Z6 are comprised in respective ranges. The ranges of the coefficients q0, ... qn referring to the zones Z1 , Z2, Z3, Z4, Z5 are given in the following five tables. Min Max

[0165] Min Max

[0166] Min Max

[0167] Min Max

[0168] Min Max

[0169] Therefore, each zone Z1 , Z2, Z3, Z4, Z5 is described by the first twelve terms of the Forbes serial expansion. The last zone Z6, i.e. , the outermost zone, has coefficients q0, ... qn of the Jacobi polynomials identically null being a simple aspherical surface, in turn described by the equation the parameters of which are given by c = curvature of the base sphere of the front or rear surface of the lens, and k = conical constant of the front or rear surface.

[0170] The maximum radii or outer radii r1 , r2, r3, r4, r5, r6, of the corresponding concentric zones Z1 , Z2, Z3, Z4, Z5, Z6 are preferably between 0.5 mm and 3.0 mm. Preferably, the outer radii of the respective zones Z1 , Z2, Z3, Z4, and Z5 can be equal to r1 = 0.4-0.5 mm, r2 = 0.7-0.9 mm, r3 = 1.27-1.47 mm, r4 = 1.70-1.90 mm and r5 = 2.15-2.35 mm, while the outer radius of the outer zone Z6 is always r6 = 3.0 mm. Merely by way of example, said maximum radii delimiting the respective zones can be: r1 = 0.5 mm, r2 = 0.82 mm, r3 = 1 .37 mm, r4 = 1 .81 mm, r5 = 2.25 mm and r6 = 3.0 mm, as shown in the graph of Figure 9.

[0171] Wanting to improve visual acuity in the FAR Field by slightly reducing performance in the NEAR Field for pupil diameters greater than = 2.7 mm, ensuring good visual quality even in low light conditions, in this example only the fourth zone Z4 and the fifth zone Z5 are the intermediate annular zones which include pupil diameters with a value always greater than 2.7 mm.

[0172] Advantageously, the coefficients q; of the Jacobi polynomials which define the refractive profile of the fourth zone Z4 are comprised in the aforesaid respective ranges (see table Z4) such that the value of the difference between the maximum value qimax and the minimum value qimin of each range, starting from the range of the coefficient qoof the first term up to the range of the coefficient qn of the twelfth term, decreases exponentially according to the following function of index i of the polynomial qimax “ qimin=3 6^ ' with coefficient a equal to 0.041 and coefficient b equal to -0.70.

[0173] Furthermore, the coefficients qi of the Jacobi polynomials which define the refractive profile of the fifth zone Z5 (see table Z5) are comprised in respective ranges such that the value of the difference between the maximum value qjmax and the minimum value q^in of each range, starting from the range of the coefficient qoof the first term up to the range of the coefficient qn of the twelfth term, decreases exponentially according to the following function of index i of the polynomial qimax “ qimin=3 6^ ' with coefficient a equal to 0.0024 and coefficient b equal to -1.00.

[0174] Figure 11a graphically depicts the maximum and minimum values for each of the Jacobi coefficients related to the annular zone Z4. Figure 11 b graphically depicts the maximum and minimum values for each of the Jacobi coefficients related to the annular zone Z5.

[0175] Figure 12a depicts the trend of the value of the difference between the maximum and minimum values for each of the Jacobi coefficients, referring respectively to the annular zone Z4 (continuous curve) and to the annular zone Z5 (dashed curve);

[0176] Figure 12b depicts the trend of the value of the difference between the maximum and minimum values of the individual Jacobi coefficients corresponding to the annular zone Z4.

[0177] Figure 12c represents the trend of the value of the difference between the maximum and minimum values of the individual Jacobi coefficients corresponding to the annular zone Z5.

[0178] The aforesaid six coaxial zones, i.e., the inner or central zone Z1 , the intermediate annular zones Z2, Z3, Z4, Z5 and the outer annular zone Z6 can completely fill the aperture ("clear aperture") of the optics or lens.

[0179] Advantageously, a spherical aberration is induced in the central zone Z1 and in the intermediate zones Z2, Z3, Z4 and Z5 in order to obtain the target TFMTF, in accordance with the coefficient tables of the Jacobi polynomials indicated above. Instead in the outer zone Z6, no spherical aberration is introduced. In fact, in this case the outermost zone Z6 has null coefficients.

[0180] The graph of Figure 10a shows the total power trend of a lens referred to this example (in the case of a lens variant with only spherical power; in this case there is no difference between tangential and sagittal power, i.e., tangential and sagittal power coincide, given the symmetry of the lens). The variation of power in a single zone is defined in order to continuously provide the best visual acuity or the best MTF for both far vision and near proximal vision, i.e. for objects situated at a distance of less than 500 mm from the eye, for different pupil diameters which can assume values between 2.5 mm and 4.5 mm.

[0181] In the graph of Figure 10b, in the case of a variant of the lens with also cylindrical or toric power, two different powers are instead distinguished, indicated with a dashed line and a continuous line (i.e., distinguished by sagittal and tangential meridian, orthogonal to each other). In particular, Figure 10b shows the power trend referring to the tangential meridian (continuous line) and the sagittal meridian (dashed line).

[0182] Difference A between the two powers is almost constant as the aperture radius (radius of the intraocular lens) varies and exactly represents the cylindrical power of the lens.

[0183] Such a separation of power (between tangential and sagittal) can be obtained on the lens of the invention by applying on the surface of the lens where there is no zonal aspheric variation with the aforesaid Jacobi polynomial coefficients, for example on the rear surface of the lens, a toric deformation compatible with the cylindrical power difference A, which is to be corrected leaving the front surface unaltered.

[0184] For the sake of simplicity and to avoid making the graphs too complicated, the following description of the total power distributions in each individual zone will refer only to the tangential meridian (continuous line), the description being the same for the sagittal meridian (dashed line), considering only the shift to take into account the cylindrical power.

[0185] The division into zones is shown more clearly in the graph of Figure 10c, where it is observed that the first zone or central zone Z1 extends from the center of the lens up to a radius of 0.5 mm at which there is a first power discontinuity. A second zone or intermediate zone Z2 extends from a radius of 0.5 mm to a radius of 0.82 mm at which there is a second power discontinuity. A third zone or intermediate zone Z3 extends from a radius of 0.82 mm to a radius of 1.37 mm at which there is a third power discontinuity. A fourth zone or intermediate zone Z4 extends from a radius of 1 .37 mm to a radius of 1 .81 mm at which there is a fourth power discontinuity. A fifth zone or intermediate zone Z5 extends from a radius of 1 .81 mm to a radius of 2.25 mm at which there is a fifth power discontinuity. A sixth zone or outer zone Z6 extends from a radius of 2.25 mm to the outer radius of 3.0 mm.

[0186] In more detail, the central zone Z1 (extending from r=0.0 mm to r=0.5 mm) includes optical powers (see Fig. 10d) that continuously vary between a power P1 at or close to the center of the lens and a power P3 at or close to the edge of the central zone. In the graph in Fig. 10d, the initial power P1 can be configured to improve far vision, or it can assume a value greater than that required for far vision, for example a power adapted to determine the best visual acuity or the best MTF for near vision for objects located at a distance of about 1.0 m from the patient's eye or for even nearer vision (about 300 mm).

[0187] In more detail, in the graph in Fig. 10d the power of the inner or central zone Z1 , up to a radius of 0.5 mm, is configured to improve near vision (at about 1.0 m) and progressively decreases from the center of the lens from the value P1 to a minimum value P2, for example at a radius of about 0.22-0.26 mm, in the presence of a slightly negative spherical aberration in a first central sub-zone (for example, to help improve far vision). Continuing towards the outside of the central zone, the power gradually increases, in the presence of a positive spherical aberration in a second central sub-zone up to a maximum value P3 at a radius of about 0.5 mm: thereby the central zone is effectively divided into two sub-zones in which the power variation alternatively contributes to far vision and near vision so that the patient has a vision quality which is more independent of the diameter.

[0188] The power in the intermediate zone Z2 (Fig. 10e), following the central one (i.e. , the zone between a radius of 0.5 mm and 0.82 mm), progressively decreases from a power value P4 to a power value P5 in the presence of a negative spherical aberration. However, since the values P4 and P5 are lower than P2, this zone overall induces a change in power such as to favor vision for objects positioned at a distance, from the patient, between the intermediate one (1.0 m) and far field.

[0189] Moving farther away from the center of the lens, in the intermediate zone Z3 (Fig. 10f), between a radius of 0.82 mm and 1.37 mm, the optical power first decreases slightly from a value P6 to a minimum value P7 and then progressively increases with the increase of the radius from the optical axis up to the extreme value P8. In fact, this intermediate zone Z3 provides a slight negative spherical aberration in the initial part thereof, for example up to a radius of about 0.94 mm, and a more pronounced positive spherical aberration in the final part thereof close to the outer edge of the zone Z3, i.e., close to the outer radius thereof. The power values between P6 and P7 contribute to improving far vision, while the value P8 contributes to improving near vision. Preferably, the power values P6 and P7 are comprised between P4 and P5 and the value P8 is greater than the maximum power value P3 of the central zone. Therefore, this intermediate zone Z3 overall has opposite behavior to that of the previous zone Z2 and contributes to maintaining the best visual acuity or the best MTF for both far vision and near vision independently of pupil diameter.

[0190] Advantageously in the intermediate zone Z4 (Fig. 10g), between a radius of 1.37 mm and a radius of 1 .81 mm, the power increases slightly from a value P9 to a value P10 in the presence of a positive spherical aberration; in this case, the power values P9 and P10 contribute more to improving the quality of vision in the intermediate region, with a target distance greater than 2.0 m.

[0191] Advantageously in the intermediate zone Z5 (Fig. 10h), between a radius of 1.81 mm and a radius of 2.25 mm, the power decreases slightly from a value P11 to a value P12 in the presence of a negative spherical aberration; advantageously in this case the power values P11 and P12 contribute to improving far vision only. In fact, the power values P11 and P12 are slightly lower than the value P9 of the intermediate zone Z4 and this contributes to improving the quality of vision in the far region (Far Field).

[0192] In the outer zone Z6 (Fig. 10i), between a radius of 2.25 mm and a radius of 3.0 mm, there is an aspherical monofocal profile with a power such as to reduce, correct or cancel the positive spherical aberration of the cornea. Preferably, the power gradually decreases from a value P13 to a value P14 as the radius from the optical axis increases, so as to partially compensate the positive spherical aberration of the cornea.

[0193] The relative trend of the powers as a function of the pupil radius, made in the three outermost zones, i.e. , from the intermediate zone Z4 to the outer zone Z6 between a pupil radius of 1 .37 mm and an outer radius of 3.0 mm, are shown separately for greater clarity in the graph of Figure 10j.

[0194] Figures 13 to 18 depict the Through Focus Modulation Transfer Function TFMTF for the tangential meridian (continuous curve) and the sagittal meridian (dashed curve) at 50lp / mm and for a pupil diameter of 2.0 mm, 2.5 mm, 3.0 mm, 3.5 mm, 4.0 mm and 5.0 mm, respectively, as a function of the depth of field in the range between -1 ,0D and 4.0D of the aforesaid lens.

[0195] The disclosures of examples of lenses presented so far can be extended to the case of lens systems, if it is intended to consider specific depth of field variations with wavefronts enhanced in a complementary manner in order to obtain greater control of the depth of field variation in the event of binocular correction.

[0196] A design method is described below for an implantable or wearable corrective lens for ophthalmic use, with the purpose of producing the lens having a front surface and a rear surface, wherein the front surface or the rear surface comprises an aspheric refractive profile with circular or rotational symmetry with respect to the optical axis, wherein said aspheric refractive profile is divided into six concentric and coaxial zones (Z1 , Z2, Z3, Z4, Z5, Z6), the profile of each zone being of only refractive type and having a geometric elevation z(r) defined by a Forbes polynomial series expansion up to the twelfth term where i = index of the polynomial, which is variable from 0 to 11 , r = aperture radius of the at least one surface, which is variable from 0 to rmax, c = inverse of the radius of curvature R of the base sphere of said at least one surface, k = conical constant of said at least one surface, rmax = maximum aperture radius of said at least one surface

[0197] Qi= Jacobi polynomials of index (a=0 and (3=4) qi = coefficients of the Jacobi polynomials Qi, wherein the coefficients qi of the Jacobi polynomials to define the refractive profile of each coaxial zone all have a value equal to zero for the refractive profile of the outermost annular zone (Z6) and to non-zero for the refractive profile of a central zone (Z1 ) and of the intermediate annular zones (Z2, ... Z5); wherein the coefficients qi of the Jacobi polynomials to define the refractive profile of the intermediate annular zones, which exclusively include pupillary diameters greater than a value comprised in a range from 2.7 mm to 3.0 mm, in particular = 2.7 mm, are comprised in respective ranges such that the value of the difference between the maximum value qimax and the minimum value qimin of each range, starting from the range of the coefficient q0of the first term up to the range of the coefficient qxof the last term of said Forbes polynomial series expansion, decreases exponentially according to a first function of the index of polynomial i qimax - qimin=3 6^ ' with coefficient a comprised in a range from 0.0010 to 0.050, and coefficient b comprised in a range from -1.10 to -0.60; wherein, starting from said optical axis, a fourth zone (Z4) and a fifth zone (Z5) of said six zones are the intermediate annular zones which exclusively include pupillary diameters greater than the value wherein the coefficients q; of the Jacobi polynomials to define the refractive profile of said fourth zone (Z4) are comprised in respective ranges such that the value of the difference between the maximum value qimax and the minimum value qimin of each range, starting from the range of the coefficient q0of the first term up to the range of the coefficient qn of the twelfth term, decreases exponentially according to said first function of the index of polynomial i qimax “ qimin=3 6^ ' with coefficient a comprised in a range from 0.030 to 0.050, preferably from 0.035 to 0.045, and coefficient b comprised in a range from -0.75 to -0.60, preferably from -0.70 to -0.60 or -0.75 to -0.65; wherein the coefficients qs of the Jacobi polynomials to define the refractive profile of said fifth zone (Z5) are comprised in respective ranges such that the value of the difference between the maximum value qjmax and the minimum value qsmin of each range, starting from the range of the coefficient q0of the first term up to the range of the coefficient qn of the twelfth term, decreases exponentially according to said first function of the index of polynomial i qimax “ qimin=3 6^ ' with coefficient a comprised in a range from 0.0020 to 0.0030, and coefficient b comprised in a range from -1 .10 to -0.90, preferably from -1 .05 to -0.95; wherein the modulus of the OTF has a maximum value greater than or equal to 0.35 at the far field, for a depth of field expressed in diopters equal to 0D, at 50 Ip / mm and for a pupil diameter greater than 3.0 mm; and wherein said modulus of the OTF always has a value greater than 0.1 for a depth of field in a range between 2D and 3D (near field), at 50 Ip / mm and for a pupil diameter less than 3.0 mm.

Claims

1. CLAIMS1. An implantable or wearable corrective lens for ophthalmic use having a front surface and a rear surface, wherein the front surface or the rear surface comprises an aspheric refractive profile with circular or rotational symmetry with respect to the optical axis, wherein said aspheric refractive profile is divided into at least three concentric and coaxial zones (Z1 , Z2, Z3, ... Zn), the profile of each zone being of only refractive type and having a geometric elevation z(r) defined by a Forbes polynomial series expansion at least up to the third termwhere i = index of the polynomial, which is variable from 0 to x, where 2<x<11 , r = aperture radius of the at least one surface, which is variable from 0 to rmax, c = inverse of the radius of curvature R of the base sphere of said at least one surface, k = conical constant of said at least one surface, rmax = maximum aperture radius of said at least one surfaceQi= Jacobi polynomials of index (a=0 and (3=4) qi = coefficients of the Jacobi polynomials Qi, wherein the coefficients qi of the Jacobi polynomials to define the refractive profile of each coaxial zone all have a value equal to zero for the refractive profile of the outermost annular zone (Zn) and to non-zero for the refractive profile of a central zone (Z1 ) and of at least one intermediate annular zone (Z2, ... Zn-1 ); wherein the coefficients qi of the Jacobi polynomials to define the refractive profile of one or more intermediate annular zones, which exclusively include pupillary diameters greater than a value comprised in a range from 2.7 mm to 3.0 mm, are comprised in respective ranges such that the value of the difference between the maximum value qimax and the minimum value qimin of each range, starting from the range of the coefficient q0of the first term up to the range of the coefficient qxof the last term of said Forbes polynomial series expansion, decreases exponentially according to a first function of the index of polynomial iwith coefficient a comprised in a range from 0.0010 to 0.050, and coefficient b comprised in a range from -1.10 to -0.60; wherein said aspheric refractive profile is divided into six zones (Z1 , Z2, Z3, Z4, Z5, Z6), the profile of each zone having said geometric elevation z(r) defined by a Forbes polynomial series expansion up to the twelfth term, where the index of polynomial i varies from 0 to 11 ; wherein, starting from said optical axis, a fourth zone (Z4) and a fifth zone (Z5) of said six zones are the intermediate annular zones which exclusively include pupillary diameters greater than the valuewherein the coefficients qi of the Jacobi polynomials to define the refractive profile of said fourth zone (Z4) are comprised in respective ranges such that the value of the difference between the maximum value qimax and the minimum value qimin of each range, starting from the range of the coefficient q0of the first term up to the range of the coefficient qn of the twelfth term, decreases exponentially according to said first function of the index of polynomial iwith coefficient a comprised in a range from 0.030 to 0.050, preferably from 0.035 to 0.045, and coefficient b comprised in a range from -0.75 to -0.60, preferably from -0.70 to -0.60 or -0.75 to -0.65; wherein the coefficients qs of the Jacobi polynomials to define the refractive profile of said fifth zone (Z5) are comprised in respective ranges such that the value of the difference between the maximum value qjmax and the minimum value qimin of each range, starting from the range of the coefficient q0of the first term up to the range of the coefficient qn of the twelfth term, decreases exponentially according to said first function of the index of polynomial iwith coefficient a comprised in a range from 0.0020 to 0.0030, and coefficient b comprised in a range from -1 .10 to -0.90, preferably from -1 .05 to -0.95; wherein the modulus of the OTF has a maximum value greater than or equal to 0.35 at the far field, for a depth of field expressed in diopters equal to 0D, at 50 Ip / mm and for a pupil diameter greater than 3.0 mm;and wherein said modulus of the OTF always has a value greater than 0.1 for a depth of field in a range between 2D and 3D (near field), at 50 Ip / mm and for a pupil diameter less than 3.0 mm.

2. A lens according to claim 1 , wherein the coefficients qi of the Jacobi polynomials to define the refractive profile of, respectively, the central zone (Z1 ) and of one or more possible intermediate annular zones, which include pupillary diameters less than or equal to said value (|), are comprised in respective ranges such that both the maximum values qimax and the minimum values qimin have a respective sinusoidal trend modulated by an exponentially decaying amplitude.

3. A lens according to claim 2, wherein said sinusoidal trend is described by a second function of the index of polynomial iwith the coefficient A comprised in a range from 0.0032 to 0.12, the coefficient B comprised in a range from 0.20 to 1 .35, the coefficient C comprised in a range from 0.20 to 3.25, the coefficient D comprised in a range from -0.070 to 0.070, the coefficient E comprised in a range from -0.105 to 0.050, and the coefficient F comprised in a range from -0.002 to 0.002.

4. A lens according to any one of the preceding claims, wherein said front surface has said aspheric refractive profile with circular or rotational symmetry with respect to the optical axis, while said rear surface comprises at least one toric portion or consists of a toric surface; or vice versa.

5. A lens according to claim 4, wherein the spherical base power of the lens is in a range from 7.0D to 32.0D, while the cylindrical base power thereof is in a range from 1.0D to 5.0D; and wherein the additional optical power, defined as the increase in the depth of focus derived from TFMTF(d, y) at 50 Ip / mm, is at most 4.0D.

6. A lens according to any one of the preceding claims, wherein the coefficients (q0,... qn) of the Jacobi polynomials to define the refractive profile of each coaxial zone are in the range -0.07< qi <0.11 ; preferably wherein the coefficients qi of the Jacobi polynomials to define the refractive profile of the central zone or first zone (Z1 ) starting from said optical axis are comprised in the following range -0.001 < qi <0.004; the coefficients qi of the Jacobi polynomials to define the refractive profile of the second zone (Z2) startingfrom said optical axis are comprised in the following range -0.009< qi <0.015; the coefficients qi of the Jacobi polynomials to define the refractive profile of the third zone (Z3) starting from the optical axis are comprised in the following range -0.069 <qi <0.108; the coefficients qi of the Jacobi polynomials to define the refractive profile of the fourth zone (Z4) starting from said optical axis are comprised in the following range -0.028 < qi <0.015; and the coefficients qi of the Jacobi polynomials to define the refractive profile of the fifth zone (Z5) starting from said optical axis are comprised in the following range -0.018< qi <0.005.

7. A lens according to claim 1 , wherein the coefficients qi of the Jacobi polynomials to define the refractive profile of, respectively, the central zone or first zone (Z1 ) and of a second zone (Z2) and third zone (Z3) which are two intermediate annular zones which include pupillary diameters less than or equal to said value (|), are comprised in respective ranges such that both the maximum values qimax and the minimum values qimin have said respective sinusoidal trend modulated by an amplitude that exponentially decays.

8. A lens according to claim 7, wherein for the first zone (Z1 ) said trend is described by said second function of the index of polynomial iwith the coefficient Ai comprised in a range from 0.0032 to 0.0040, the coefficient Bi comprised in a range from 1.25 to 1.35, the coefficient Ci comprised in a range from 0.20 to 0.60, the coefficient Di comprised in a range from 0.005 to 0.070, the coefficient Ei comprised in a range from -0.105 to 0.005, and the coefficient Fi comprised in a range from -0.002 to 0.002; wherein for the second zone (Z2) said trend is described by said second function of the index of polynomial iwith the coefficient A2 comprised in a range from 0.0075 to 0.0175, the coefficient B2 comprised in a range from 0.20 to 1.10, the coefficient C2 comprised in a range from 0.70 to 3.25, the coefficient D2 comprised in a range from -0.070 to -0.010, the coefficient E2 comprised in a range from -0.010 to 0.050; and the coefficient F2 comprised in a range from -0.002 to 0.002;and wherein for the third zone (Z3) said trend is described by said second function of the index of polynomial iwith the coefficient A3 comprised in a range from 0.08 to 0.12, the coefficient B3 comprised in a range from 0.35 to 0.52, the coefficient C3 comprised in a range fromI .00 to 1.30, the coefficient D3 comprised in a range from -0.015 to 0.005, the coefficient E3 comprised in a range from 0.010 to 0.025, and the coefficient F3 comprised in a range from -0.002 to 0.002.

9. A lens according to any one of claims 1 or 7 or 8, wherein only in the central zone (Z1 ) and in the four intermediate annular zones (Z2, Z3, Z4, Z5), a spherical aberration described according to said Forbes polynomial series expansion is introduced for the purpose of extending the depth of field; and wherein an optical power discontinuity is provided between each coaxial zone and the subsequent one.

10. A lens according to any one of claims 1 or 7 or 8 or 9, wherein the total optical power, as the radius increases in the fourth zone (Z4), increases from a value P9 to a value P10 in the presence of a positive spherical aberration in said fourth zone (Z4); while the total optical power in the fifth zone (Z5) decreases from a value P11 to a value P12 in the presence of a negative spherical aberration in said fifth zone (Z5); preferably wherein both the value P11 and the value P12 are lower than the value P9 of the fourth zone (Z4).I I . A lens according to any one of claims 1 or 7 or 8 or 9, wherein the total optical power of the first zone or central zone (Z1 ) starting from the center of the lens, as the radius increases,- decreases from a first value P1 to a second value P2 in the presence of a negative spherical aberration in a first central sub-zone;- and increases from said second value P2 to a third value P3 at the first outer radius r1 of said first zone, in the presence of a positive spherical aberration in a second central sub-zone;preferably wherein the total optical power in the second zone (Z2), starting from the first outer radius r1 , decreases from a fourth value P4 to a fifth value P5 in the presence of a negative spherical aberration in said second zone (Z2); preferably wherein the fourth value P4 is less than the second value P2; preferably wherein the total optical power in the third zone (Z3) starting from the second outer radius r2 of said second zone- decreases from a sixth value P6 to a seventh value P7 in the presence of a negative spherical aberration in an initial part of said third zone (Z3);- and increases from said seventh value P7 to an eighth value P8 at the third outer radius r3 of said third zone, in the presence of a positive spherical aberration in a final part of said third zone (Z3), preferably wherein both the sixth value P6 and the seventh value P7 are comprised in the range comprised between the fourth value P4 and the fifth value P5, and wherein the eighth value P8 is greater than the third value P3 of the central zone (Z1 ); preferably wherein the total optical power in the fourth zone (Z4) starting from the third outer radius r3 increases from a ninth value P9 to a tenth value P10 at the fourth outer radius r4 of said fourth zone, in the presence of an overall positive spherical aberration in said fourth zone (Z4); preferably wherein the total optical power in the fifth zone (Z5) starting from the fourth outer radius r4 decreases from an eleventh value P11 to a twelfth value P12 at the fifth outer radius r5 of said fifth zone, in the presence of an overall negative spherical aberration in said fifth zone (Z5); preferably wherein both the eleventh value P11 and the twelfth value P12 are lower than the ninth value P9 of the fourth zone (Z4); preferably wherein the optical power in the sixth zone or outer annular zone (Z6) starting from the fifth outer radius r5 decreases from a thirteenth value P13 to a fourteenth value P14 at the sixth outer radius r6 of said sixth zone.

12. A lens according to any one of the preceding claims, made of hydrophilic or hydrophobic acrylic material, preferably a hydrogel copolymer of 2-hydroxyethyl methacrylate (2-HEMA) and 2-ethoxyethyl methacrylate (EOEMA) with a watercontent of 20-30%, for example 25%, including a hydroxyphenyl triazine (HPT)- based UV absorber.

13. A lens according to any one of the preceding claims, wherein said modulus of the OTF always has a value greater than 0.15 for a depth of field in a range between 2D and 3D (NEAR field), at 50 Ip / mm and for a pupil diameter less than or equal to 2.5 mm.

14. A lens according to any one of the preceding claims, wherein said modulus of the OTF always has a value greater than 0.20 for a depth of field in a range between 2D and 3D (NEAR field), at 50 Ip / mm and for a pupil diameter less than or equal to 2.0 mm.

15. A design method for an implantable or wearable corrective lens for ophthalmic use, with the purpose of producing the lens having a front surface and a rear surface, wherein the front surface or the rear surface comprises an aspheric refractive profile with circular or rotational symmetry with respect to the optical axis, wherein said aspheric refractive profile is divided into at least three concentric and coaxial zones (Z1 , Z2, Z3, ... Zn), the profile of each zone being of only refractive type and having a geometric elevation z(r) defined by a Forbes polynomial series expansion at least up to the third termwhere i = index of the polynomial, which is variable from 0 to x, where 2<x<11 , r = aperture radius of the at least one surface, which is variable from 0 to rmax, c = inverse of the radius of curvature R of the base sphere of said at least one surface, k = conical constant of said at least one surface, rmax = maximum aperture radius of said at least one surfaceQi= Jacobi polynomials of index (a=0 and (3=4) qi = coefficients of the Jacobi polynomials Qi, wherein the coefficients qi of the Jacobi polynomials to define the refractive profile of each coaxial zone all have a value equal to zero for the refractive profile of theoutermost annular zone (Zn) and non-zero for the refractive profile of a central zone (Z1 ) and at least one intermediate annular zone (Z2, ... Zn-1); wherein the coefficients qi of the Jacobi polynomials to define the refractive profile of one or more intermediate annular zones, which exclusively include pupillary diameters greater than a value comprised in a range from 2.7 mm to 3.0 mm, are comprised in respective ranges such that the value of the difference between the maximum value qimax and the minimum value qimin of each range, starting from the range of the coefficient q0of the first term up to the range of the coefficient qxof the last term of said Forbes polynomial series expansion, decreases exponentially according to a first function of the index of polynomial i qimax - qimin=3 6^ ' with coefficient a comprised in a range from 0.0010 to 0.050, and coefficient b comprised in a range from -1.10 to -0.60; wherein said aspheric refractive profile is divided into six zones (Z1 , Z2, Z3, Z4, Z5, Z6), the profile of each zone having said geometric elevation z(r) defined by a Forbes polynomial series expansion up to the twelfth term, where the index of polynomial i varies from 0 to 11 ; wherein, starting from said optical axis, a fourth zone (Z4) and a fifth zone (Z5) of said six zones are the intermediate annular zones which exclusively include pupillary diameters greater than the valuewherein the coefficients qi of the Jacobi polynomials to define the refractive profile of said fourth zone (Z4) are comprised in respective ranges such that the value of the difference between the maximum value qimax and the minimum value qimin of each range, starting from the range of the coefficient q0of the first term up to the range of the coefficient qn of the twelfth term, decreases exponentially according to said first function of the index of polynomial i qimax “ qimin=3 6^ ' with coefficient a comprised in a range from 0.030 to 0.050, preferably from 0.035 to 0.045, and coefficient b comprised in a range from -0.75 to -0.60, preferably from -0.70 to -0.60 or -0.75 to -0.65; wherein the coefficients qs of the Jacobi polynomials to define the refractive profile of said fifth zone (Z5) are comprised in respective ranges such that the value of thedifference between the maximum value qimax and the minimum value qimin of each range, starting from the range of the coefficient q0of the first term up to the range of the coefficient qn of the twelfth term, decreases exponentially according to said first function of the index of polynomial i qimax - qimin=3 6^ ' with coefficient a comprised in a range from 0.0020 to 0.0030, and coefficient b comprised in a range from -1 .10 to -0.90, preferably from -1 .05 to -0.95; wherein the modulus of the OTF has a maximum value greater than or equal to 0.35 at a depth of field of 0D (far field), at 50 Ip / mm and for a pupil diameter greater than 3.0 mm; and wherein said modulus of the OTF always has a value greater than 0.1 for a depth of field in a range between 2D and 3D (near field), at 50 Ip / mm and for a pupil diameter less than 3.0 mm.

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