Addition of a third degree optical function to an optical element, for example, a lens, provides Extended Depth of Field, EDoF. Such function extends the single focal spot on the optical axis into an extended focal band, along the optical axis. Such extension of focus can be applied, for example, to, continuously, extend DoF for human vision, ideally from far to near, to reading distance. For example, progressive glasses in spectacles and progressive optical surfaces in intraocular lenses, are, largely, based on said optical principle as disclosed in US7025454 (2006) and in a pending patent application US2014/0257480 (2014). Both documents disclose the use of single or multiple third degree, cubic, optical surfaces, albeit in different configurations.

Theoretical and mathematical considerations regarding such single cubic surfaces are provided by J. Opt. Soc. Am A, Vol.26, No.4. The present document discloses ophthalmic lenses for Extended Depth of Field, EDoF, henceforth: "lens", a lens to be positioned anywhere between the object and the retina of the eye, which lenses incorporate at least one optical element with a combination of, at least two, optical surfaces with one surface positioned on the anterior side of the optical element and the other optical surface on the posterior side of the optical element. Said optical surfaces include at least one optical shape according to a polynomial of the fourth degree, for example, in the most basic form, without any additional terms:

z = S ₀ (x, y) = A(x ⁴ /4 + xy ³ ) , with z being the sag of the optical surface, with x and y the values of X,Y coordinates presenting the plane perpendicular to the optical axis, the Z coordinate, and with A being a constant. Said optical surfaces can be arranged such that the arrangement a third order optical function, as in: S _l - S _Q (x + Ax, y) and

S ₂ - S _Q (x + Ax, y) , of which a combination results in S _l - S ₂ ~ 2AAx(x ³ + y ³ ) which third degree optical function provides said EDoF.

Such a lens may be embodied as an intraocular lens or as a spectacles lens.

As stated before, the lens may comprise a single optical element only. In this case the optical shape according to the fourth degree may be located on one of the two optical surfaces, but may also be distributed over both optical surfaces. Alternatively, such lenses can incorporate at least two optical elements with each element with at least one optical surface with an optical shape according to a polynomial of the fourth degree. Said optical surfaces can be distributed over any combination of anterior sides and posterior sides of said optical elements in an arrangement to provide a third degree optical function, which is also known as a third degree wavefront. More in particular the lens may comprise at least two optical elements and each element may comprise at least one optical surface with an optical shape according to a polynomial of the fourth degree. It is however also possible that the optical surfaces are located on one of the optical elements only and that the other optical element has other purposes.

Such lenses can also provide, by movement of at least one of the optical elements, a variable extension of DoF, and/or variable focus, and/or variable spherical aberration. Such movement can be achieved, but not restricted to, principles as disclosed in US2009062912 and WO2005084587, and the same concept, with various adaptations in, for example, US2014074233, WO2014058316, EP2765952, NL2012257278, US2010131955, US2010106245, NL1029548 and references made therein and related documents, which principles have been shown to function in the human eye. Consequently a preferred embodiment provides a lens of the kind referred to above, wherein its optical power is variable by relative movement of the optical elements. Of course the present invention provides a range of optical strengths, and the above expression refers to the variability of said range. According to a preferred embodiment the optical elements are adapted to be moved relatively in the direction of the optical axis, as is disclosed in some of the references cited above, but it is also possible that the optical elements are adapted to be moved relatively in the direction perpendicular to the optical axis. So, the lens can provide a fixed degree of EDoF in combination with a fixed degree of correction of at least one aberration of any degree, or, alternatively, the lens can provide a variable degree of EDoF in combination with a fixed degree of correction of at least one aberration of any other degree, or, alternatively, the lens can provide a variable degree of correction of EDoF, in combination with a variable degree of correction of at least one aberration of any degree. The lens providing variable EDoF or variable corrections can be driven by any driver means of which the degree of driving

corresponds to the degree of correction of said aberration, which driver means can be, occasional, outside intervention, for example, surgical intervention, to occasionally adjust any of said lens parameters providing a lens which is adjustable post operatively, or, alternatively, the lens can be driven by any component in the eye, for example, the ciliary muscle of the eye or any mechanical driver means implanted in the eye, mechanically coupled to the lens. With all driving means the degree of correction which degree depends on the degree of driving.

In the preferred embodiment said lenses can have a combination of fourth degree optical surfaces which optical surfaces have the same amplitude, the same A-constant as given in the formulas above, so which optical surfaces are identical. So, both the polynomial functions of the fourth degree provide the same fourth degree amplitude. However, for the combination to obtain the desired a desired third degree function the optical surfaces of said combination should be arranged in the X-Y plane at an offset, meaning: at least one of the surfaces should be decentred in the X-Y plane versus the optical axis, the Z- axis. The degree of offset provides a corresponding degree, preferably the desired degree of amplitude of the third degree.

Alternatively, in another embodiment, said lenses can have fourth degree optical surfaces which have different amplitudes. In such arrangements an offset can be applied, but such offset is not necessary to obtain a desired third degree optical function. The optical surfaces of the fourth degree of said combination can be symmetrically arranged in the X-Y plane with the degree of difference in amplitude provides a corresponding degree of amplitude of the third order optical function. However, in such arrangements fourth degree rest terms remain which might degrade the optical quality.

The lens can also comprise at least one additional optical surface with an optical shape according to any polynomial of any degree which optical shape is adapted to provide correction of any aberration of the eye. For example, the lens can comprise at least one additional optical surface with an optical shape according to a polynomial of an even degree, for example, a parabola, as in z = S Ax, y) = C(x ² + y ² ) or a sphere, as in z— S _s ( x, y) - cr ² / 1 + 1 - c ² r ² or combinations of parabolas and/or spheres, in any combination, to provide correction of focusing error of the eye, in case of an intraocular lens, for the refractive error of the eye. Alternatively, the lens can comprise at least two additional optical surfaces with an optical shape according to a polynomial of an odd degree to provide correction of focusing error of the eye, for example, two third degree surfaces as in

z - S _h (x, y) - B(x ³ 13 + x ³ ) , with two of such optical surfaces forming a focusing lens, an "Alvarez lens" by combining S ₃ - S _h (x + Ax, y) and S ₄ - S _h {x - Ax, y) and S ₃ - S ₄ ~ 2B(x ² + y ² )Ax which has the optical function of a parabolic focusing lens.

Also, the lens can comprise at least one additional optical surface with any optical shape which is adapted to provide correction of astigmatism of the eye.

Lenses disclosed in the present document can have a number of ophthalmic

applications. For example, the lens can be an intraocular lens, surgically implanted in the eye, for example implanted in a phakic eye, functioning in combination with the natural lens of the eye, as a piggy-back lens or anterior chamber lens. Alternatively, such lens can be an intraocular lens implanted in a pseudophakic eye, functioning in combination with another intraocular lens, again as a piggyback lens or anterior chamber lens or, alternatively, such lens can be implanted in an aphakic eye, an eye from which the natural lens is removed and not replaced by any intraocular lens.

Alternatively, such lens can be a contact lens positioned on top of the cornea of the eye, or, alternatively, such lens can be a spectacle lens positioned in front of the eye. Multiple optical elements can be the same material or, alternatively, of different materials with, for example, two different materials with different refractive indices. In case of single element lenses, each optical surface can be of the same material or, alternatively, of different materials. A method of providing an ophthalmic lens, with the method providing EDoF to the eye by a lens, which lens comprises at least one optical element which element comprises a combination of, at least two, optical surfaces with one surface positioned on the anterior side of the optical element and the other optical surface on the posterior side of the optical element provides a lens comprising said optical surfaces which each includes at least one optical shape according to a polynomial function of the fourth degree with said optical surfaces arranged such that the arrangement is adapted to provide an EDoF. Alternatively, a method can provide such a lens comprising two optical elements which elements each comprise at least one optical surface according to a polynomial of the fourth degree which surfaces can be distributed over any combination of anterior sides and posterior sides of said optical elements.

With the Figures: Figure 1 shows a planar base plate, 1, fitted with two, 2,3, fourth degree optical surfaces in an arrangement which provides a third degree optical function, and embodiment suitable for, for example, a piggy-back intraocular lens. Figure 2 as in Figure 1, with a parabolic lens, 4, added to provide fixed optical focusing power, an embodiment suitable for, for example, an intraocular lens for implant in an aphakic eye. Figure 3 as in Figure 2, with the parabolic lens, 4,5, distributed over the two sides of the construction. Figure 4 as in Figure 1, with two third order optical surfaces, 6, 7, added to provide a fixed power focusing lens. Figure 5 shows an embodiment with two base plates, 8, 9, two four degree optical surfaces, 2, 3, and a lens of fixed optical focusing power, 10. Figure 6 as Figure 5, with added two, 10, 11, third degree optical surfaces to provide said fixed optical power.

So, in summary, the present document discloses an ophthalmic lens for extended depth of field, a lens to be positioned anywhere between the object and the retina of the eye, which lens incorporates at least one optical element comprising a combination of at least two optical surfaces with one such surface positioned on the anterior side of the optical element and the other such surface positioned on the posterior side of the optical element with said optical surfaces including at least one optical shape according to a polynomial of the fourth degree with said optical surfaces arranged such that the arrangement provides an optical function according to a polynomial of the third degree for extended depth of field, or, alternatively, a lens incorporating at least two optical elements with each element incorporating at least one optical surface with an optical shape according to a polynomial of the fourth degree which surfaces are distributed over any combination of anterior sides and posterior sides of said optical elements, with both alternatives, optionally, also comprising at least one additional optical surface with an optical shape according to any polynomial of any degree which optical shape is adapted to provide any optical function for correction of any aberration of the eye, which at least one additional optical surface can have an optical shape provide correction of focusing aberration of the eye, or, alternatively, with at least two additional optical surfaces with an optical shape to provide correction of focusing aberration of the eye, and/or at least one additional optical surface with any optical shape which is adapted to provide correction of astigmatism aberration of the eye, the lens combined with a method of providing an ophthalmic lens, with the method providing extended depth of field to the eye by a lens, which lens comprises at least one optical element which element comprises a combination of, at least two, optical surfaces with one surface positioned on the anterior side of the optical element and the other optical surface on the posterior side of the optical element with the method providing a lens comprising said optical surfaces which each includes at least one optical shape according to a polynomial function of the fourth degree with said optical surfaces arranged such that the arrangement is adapted to provide an extended depth of field, or, alternatively, with the method providing a lens which comprises two optical elements which elements each incorporate at least one optical surface according to a polynomial of the fourth degree which surfaces can be distributed over any combination of anterior sides and posterior sides of said optical elements.