ES3041207A1 - DESIGN METHOD FOR AN OPTICAL ELEMENT FOR PRESBYOPIA CORRECTION AND OPTICAL ELEMENT DESIGNED ACCORDING TO THE SAME (Machine-translation by Google Translate, not legally binding) - Google Patents

Abstract

Method for designing an optical element for presbyopia correction and optical element designed according thereto. Method for designing an optical element and said optical element for presbyopia correction by depth of focus extension, comprising selecting an optical path difference (W(r,θ)) and/or a surface topography (Δ(r,θ)) of the optical element, which is expressed as {IMAGE-01} where the values of n, N and A are constants chosen from n >=3, N >=3 and {IMAGE-02}. The value of A being at least as high as such that an angular average value of a phase transfer function (PTF) of the ocular optical system formed by the optical element is in absolute value less than or equal to π/2, over the entire spatial frequency range from 0 cycles/degree to 20 cycles/degree, and at least at an eye-to-object distance (d) in the range of 0.3 m to 6 m. (Machine-translation by Google Translate, not legally binding)

Description

DESCRIPTION

DESIGN METHOD FOR AN OPTICAL ELEMENT FOR PRESBYOPIA CORRECTION

AND OPTICAL ELEMENT DESIGNED ACCORDING TO THE SAME

OBJECT OF THE INVENTION

The present invention relates to an optical element for presbyopia correction by means of extended depth of focus (EDOF). This presbyopia correction technique is based on generating an elongated focus in the direction of light propagation that makes it possible to focus on objects located at different distances from the eye within a suitable range of clear vision.

BACKGROUND OF THE INVENTION

Presbyopia, commonly known as age-related farsightedness, is the progressive physiological decline in the eye's ability to focus with age, resulting in increased difficulty seeing near objects clearly. This reduction in the eye's ability to focus is due to a decrease in the elasticity of the lens, particularly its nucleus, which undergoes the greatest deformation during the focusing process.

Like other refractive errors such as myopia, hyperopia, or astigmatism, presbyopia can be corrected with glasses, contact lenses, intraocular lenses, or refractive surgery. For presbyopia correction, the use of optical devices such as monofocal, multifocal, and progressive lenses is well-established, and in the case of contact lenses and intraocular lenses, extended depth of focus (EDOF) lenses are also common.

Extended depth-of-focus lenses are designed by selecting a suitable lens surface topography to provide an optical profile that creates an elongated focus. This allows objects located at varying distances from the eye, within the range of clear vision provided by the optical element, to appear sufficiently in focus.

In contrast, extended depth of focus lenses exhibit a decrease in image contrast compared to single-vision lenses, because instead of bringing all the light rays from the object together on a single plane, they distribute the light between adjacent planes.

Various extended depth-of-focus lens designs are known for correcting presbyopia. Currently, the most common designs available, due to their adequate optical performance, are those based on lenses that introduce a first-order spherical aberration. Within this group are lenses with a surface topography that can be expressed in polar coordinates (r,θ), for 0 < r < 1 and 0 < 0 < 2 u, with respect to a pupillary tangent plane, as A(r, θ) = 3 • (6r⁴ - 6r²)·m.

However, known extended depth-of-focus lens designs have several limitations. One limitation is the dependence of some designs on the user's pupil diameter, meaning that the quality of the displayed image, as well as the range of clear vision they provide, depends on that diameter.

Another limitation is their vulnerability to artifacts or aberrations, such as chromatic aberrations, which are due to their dependence on visible wavelengths, or coma aberrations. These artifacts or aberrations degrade the displayed image, substantially reducing the quality and comfort of viewing.

On the other hand, although presbyopia can be considered an independent process from refractive errors of the eye such as myopia, hyperopia and astigmatism, the known designs of extended depth of focus lenses also have the drawback that they are not able to correct different powers of the same type of refractive error, whether myopia, hyperopia or astigmatism, with the same lens.

Furthermore, in the case of astigmatism, the known optical elements used have the additional limitation of their sensitivity to decentration or rotation, which affects the improvement in visual quality. To overcome this limitation, contact lenses or intraocular lenses must include stabilization and anchoring systems, which complicate and increase the cost of their design and manufacture.

The present invention aims to overcome the known limitations of existing optical elements for presbyopia correction in the prior art. In particular, the present invention seeks to design and obtain optical elements for presbyopia correction by extending the depth of focus (EDOF) that are insensitive to changes in the user's pupil diameter, changes in the wavelength of light, and decentration.

EXPLANATION OF THE INVENTION

To achieve the aforementioned objective, as well as additional technical advantages that may be derived from this descriptive memorandum, the invention provides a design method that allows obtaining optical elements or lenses for presbyopia correction by extending the depth of focus.

The design method according to the invention comprises selecting a surface topography of the optical element that is expressed in polar coordinates (r,θ) as A(r , θ) = A·r n·cos(N·θ y ) , for 0 < r < 1 and 0 < θ <2n.

In the context of the invention, surface topography refers to the height of the optical element at each point relative to a base surface, which may be, for example, a curved surface, with respect to the coordinates of a reference plane. Therefore, surface topography can be defined by the thickness of the optical element.

For example, in an embodiment where the optical element is shaped like a contact lens, the reference plane may be constituted by the pupillary tangent plane of the eye and the surface topography by the thickness of the lens with respect to the curved base surface that rests on the cornea of the eye.

The parameters that define the characteristic surface topography of the invention, which is given by the expression A(r ,θ) = A·r n·cos(N·θ φ), are the constants A, n, N and φ. According to the invention, these parameters are chosen to meet the following requirements.

The parameter φ can take any value greater than or equal to 0 and less than 2n, and the values of n, N and A are chosen from: n>3; N>3, in particular N being an integer; and A ^0, in particular A >0.

Furthermore, the value of A must be at least as high as that, starting from a phase transfer function (PTF) of the ocular optical system formed by the optical element, an angular average value of said function for the different wavelengths of a light beam, with at least one visible wavelength, is in absolute value less than or equal to n/2, preferably n/4 and more preferably n/8.

This condition for the value of A must be verified across the entire range of spatial frequencies from 0 cycles/degree to 20 cycles/degree, preferably to 25 cycles/degree and more preferably to 30 cycles/degree, and at least at an eye-to-object distance in the range of 0.3 m to 0.4 m, preferably also from 0.4 to 1.0 m and more preferably also from 1.0 to 6.0 m.

The prescribed spatial frequency ranges, up to 20 cycles/degree, preferably up to 25 cycles/degree and more preferably up to 30 cycles/degree, correspond to the spatial frequencies presented by a decimal visual acuity optotype of 0.8.

Phase transfer functions (PTF) for the optical system formed by the eye and an optical element defined by a surface topography can be obtained by computer simulation, in a way that is already known to the expert in the field.

As is known, every optical system, such as the one made up of the eye and the optical element for presbyopia correction, can be expressed by a function called the optical transfer function (OTF) in terms of its spatial frequency distribution.

The optical transfer function (OTF) can be expressed as OTF = MTF·eiPTF, where MTF is the so-called modulus of the transfer function (MTF, “Modulation Transfer Function”). The PTF function reports the phase that the optical system adds to a certain spectral component.

The phase transfer function (PTF) is related to the optical path difference W(r,0) that the optical element introduces into the optical system and can be expressed in general as W(r,θ) = (k(r,θ,X) -1) · A(r,θ), where k(r,0,A) represents the distribution of the refractive index of the optical element, which in general can also depend on the wavelength (A), and A(r,0) is the topography of the surface of the element, expressed, for example, in polar coordinates r, 0.

According to the invention, it has been found that, surprisingly, by selecting a surface topography of the optical element of the form A(r,d) = A·r n·cos(N·0 φ) and choosing the parameters A, n, N and φ as indicated, it is possible to obtain designs of presbyopia correction optical elements that offer adequate sharpness, absence of artifacts or aberrations and display contrast.

Furthermore, surprisingly, it has also been found that, in general, by selecting an optical path difference (W(r,0)) of the optical element of the form W(r,θ) = A ^ rn^cos(N·θ φ), applying the same selection criteria for the parameters A, n, N and φ that have been indicated for A(r,θ), it is also possible to obtain designs of presbyopia correction optical elements that offer adequate sharpness, absence of artifacts or aberrations and display contrast.

In particular, with the optical element designs that can be obtained according to the invention, it is possible to reduce the presence of chromatic aberrations, as a consequence of their reduced sensitivity to visible wavelengths.

Furthermore, it has been found that the optical element designs that can be obtained have reduced or zero sensitivity to the user's pupil diameter, so that, advantageously, the improvement in sharpness, absence of artifacts or aberrations and visual contrast do not depend on the pupil diameter.

Another property of the designs obtainable according to the invention is that, given certain values of A, n, and N, the designs exhibit analogous behavior for any chosen value of φ. That is, for example, an optical element design with a surface topography given by A(r,θ) = 32·r 3·cos(4·θ) pm, exhibits analogous behavior to that of a surface topography given by, for example, A(r, θ) = 32·r 3· cos(4 ■θn /4 )pm.

This property gives rise to the advantage of the designs of the invention, which consists of the tolerance they exhibit against decentration or rotation, which facilitates their implementation in the form of contact lenses or intraocular lenses and allows for improved visual quality.

This advantage has a special impact when the presbyopia correction of the optical element is combined with an astigmatism correction, since, as is generally known, the astigmatism-correcting optical element loses effectiveness when rotated and requires a predetermined orientation.

In this respect, the designs of presbyopia correction optical elements according to the invention allow for the integration of refractive errors such as myopia, hyperopia, or astigmatism within the element itself, without altering the presbyopia correction properties or improving sharpness, absence of artifacts or aberrations, and visual contrast. This can be achieved by selecting a curvature of the base surface to provide adequate power for correcting the refractive errors. The base surface refers, in particular, to the surface against which the surface topography of the optical element is expressed.

In short, the design method according to the invention as described makes it possible to selectively obtain optical elements for presbyopia correction by depth of focus extension that present improvements over those known in the prior art.

Characteristically, the invention provides high selectivity by allowing the selection of optical element designs from a wide range of possible designs, technically defined by multiple parameters and, in particular, based on the phase transfer function (PTF).

Thanks to the invention, through the phase transfer function (PTF) it is possible to directly check if the sum of the Fourier harmonics that construct the retinal image is formed correctly, so that the phase shift introduced by the optical element is adequate, when it does not exceed the average angular value in absolute value of n/2.

According to more particular embodiments of the invention, the design method may include additional steps that allow for obtaining optical element designs in a more selective manner.

In this regard, the invention contemplates, for example, that, starting from values of n, N, and A chosen as indicated, N is increased to substantially reduce the appearance of artifacts compared to the initially selected optical path difference or surface topography, for the range of eye-to-object distances considered and with respect to an optotype of 0.8 decimal visual acuity. According to a variant of this embodiment, in addition to increasing N, A is also increased with the same objective.

According to another embodiment, starting from the values of n, N, and A chosen as indicated, n is increased to substantially increase the contrast compared to the initially selected optical path difference or surface topography, for the range of eye-to-object distances considered and with respect to an optotype with a visual acuity of 0.8 decimal. Likewise, according to a variant of this embodiment, in addition to increasing n, A is also increased with the same objective.

These realizations make it possible, in particular, to effectively select the most suitable optical path difference or surface topography iteratively within the variety of possible designs.

In another aspect, the present invention also relates to a computer program for designing an optical element for presbyopia correction. The computer program comprises instructions such that, when executed by a computer, it implements a design method for selecting an optical path difference or surface topography of the optical element as described.

According to another additional aspect of the invention, the present invention also relates to the optical element itself for presbyopia correction, which has an optical path difference or surface topography that is obtainable by a design method, or a computer program, as described.

The invention contemplates that the optical element for presbyopia correction can be, for example, a lens, such as a contact lens or an intraocular lens, obtained by corneal carving or incorporated into an intrastromal device.

With regard to corneal reshaping, according to another aspect, the invention also relates to a laser refractive surgery device for performing such corneal reshaping. According to the invention, the device is configured to emit laser pulses onto the cornea to produce, by means of corneal reshaping, an optical path difference or surface topography that is achievable by a design method, or a computer program, as described.

According to the invention, obtaining a specific optical path difference of the optical element, such as W(r , θ) = A · r n • cos (N • θ φ), can be done by selecting a variable refractive index function (k(r,θ)).

Local differences in the refractive index (k(r,θ)) can be achieved by various methods, each of which is well-known. For example, one method is ion exchange. This method involves exchanging ions from the material medium for salts, usually using masks that allow local changes in the refractive index through localized ion exchange.

A second known method for obtaining optical elements with variable refractive indices (k(r,θ)) is by deposition of layers of material with different refractive indices in localized areas. Another known method is by selective photopolymerization of the material in the different areas of the optical element where the refractive index is locally modified.

According to the invention, the optical path difference of the form W(r, θ) = A • r n • cos(N • θ φ) can also be obtained by generating diffraction in the optical element, i.e., by using diffractive optical elements. In diffractive optical elements, the diffraction of light is used to achieve a specific optical path difference. For example, a diffraction grating is a diffractive optical element. There are also various known methods for obtaining diffractive optical elements.

The invention contemplates that the optical path difference can be provided in combination, by means of optical elements that provide the optical path difference by refraction and/or by diffraction. For example, with one optical element provided with a refractive surface (in particular, by means of a specific surface topography) and the other with a diffractive surface.

One way to obtain a diffractive optical element is to add a periodic function to the refractive optical element, which generates a specific optical path difference. This periodic function can be an amplitude function, modifying the field amplitude, or a periodic function that is added to the optical path difference.

Another way to generate a diffractive element is to construct a function for generating the optical path difference obtained by restricting the values of the function that describes the optical path difference between [-A, A]. This diffractive optical path function (W'(r,0)) can be obtained using the expression W'(r,0) = W(r,0) - 2n*

R[] being an operator that acts on its argument by rounding towards the

negative infinity.

Optical elements for presbyopia correction can be manufactured using existing techniques such as turning, molding, or centrifugal casting. Surface etching, photosculpting using transmission masks and photosensitive materials, or laser etching can also be employed.

The manufacturing process may employ, for example, materials normally used in the manufacture of contact lenses or intraocular lenses, such as hydroxyethyl methacrylate, polymethyl methacrylate, siloxanylstyrene and fluoromethacrylate compounds, silicone hydrogel or methacrylate/acrylate copolymer.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention is described in greater detail below for illustrative and non-limiting purposes, as well as with respect to a preferred embodiment by way of example, with reference to the accompanying drawings. In the drawings:

Figures 1 and 2 show a side cross-sectional view of an eye in which an optical element for presbyopia correction is located in the form of a contact lens according to an embodiment of the invention.

Figure 3 represents an example of lens design obtained according to the invention, whose surface topography is given by A(r, 0) = 32 • r 3 • cos(4 • 0) m.

Figure 4 represents a lens design known in the prior art, whose surface topography is given by A(r, 0) = 3 • [6r4 - 6r 21]¡¿m.

Figure 5 shows a simulated visualization of a visual acuity optotype of 0.8 by means of the known lens design represented in Figure 4. The letter E of Snellen was chosen as the optotype used in the simulation.

Figure 6 shows the polychromatic impulse response of the eye, for three wavelengths, 0.4806 μm, 0.5876 μm and 0.6563 μm, simulated for the known lens design depicted in Figure 4.

Figures 7, 10, 13, 16, 19, 22, and 25 show different simulated visualizations of a visual acuity optotype of 0.8 using respective lens design examples obtained according to the invention. In particular, Figure 16 corresponds to the lens design example in Figure 3. The Snellen letter E was chosen as the optotype used in the simulation.

Figures 8, 11, 14, 17, 20, 23, and 26 show the different polychromatic impulse responses of the eye for the three wavelengths considered: 0.4806 μm, 0.5876 μm, and 0.6563 μm, simulated for the respective lens design examples obtained according to the invention. In particular, Figure 17 corresponds to the lens design example in Figure 3.

Figures 9, 12, 15, 18, 21, 24, and 27, for each of these A, B, and C, show the different phase transfer functions (PTF), in angular mean value for the three wavelengths considered, 0.4806 μm, 0.5876 μm, and 0.6563 μm, simulated for the respective lens design examples obtained according to the invention. In particular, Figures 18A, 18B, and 18C correspond to the lens design example in Figure 3.

For figures 9, 12, 15, 18, 21, 24, and 27, figures A, B, and C correspond to the phase transfer function (PTF) values for pupil diameters of 5.0 mm, 3.5 mm, and 2.5 mm, respectively. The dotted, dashed, and solid lines correspond to the PTF values for object distances of 0.4 m, 1 m, and 6 m, respectively.

DETAILED DESCRIPTION OF THE INVENTION

Figure 1 shows schematically, according to a lateral cross-sectional view, an eye in which an optical element for presbyopia correction is placed in the form of a contact lens (1) positioned on the cornea (2).

The contact lens (1) has a surface topography suitable for extending the depth of focus of the optical system formed by the eye and the optical element itself. The contact lens (1) introduces a phase difference across the pupil (3) and the crystalline lens (4) that is projected onto the retina (5) of the eye.

Figure 2 schematically shows the view of Figure 1 together with an indication of the magnitudes of eye-to-object distance (d) and pupillary diameter (D) used in the context of the invention.

Figure 3 shows an example of an optical element design in the form of a contact lens (1), obtained according to the invention, whose surface topography is given, with respect to a pupillary tangent plane (31), by the expression: A(r,8) = 32·r 3· cos(4 ■ 0)^m.

The different levels of gray in the image within the circle in the figure correspond to the different heights of the lens at different points, which vary between the white points, which have minimum height, and the black points, which have maximum height.

In comparison with the previous figure, Figure 4 represents a known design of a presbyopia correction lens by depth of focus extension, of the type that introduces a first-order spherical aberration and whose surface topography is given by the expression A(r, 8) = 3·[6r4 - 6r 21]¡¿m.

Figure 5 shows the image formed by the eye on the retina (5) when viewing an optotype of visual acuity 0.8 by means of a known lens whose surface topography is that of Figure 4. The representation has been obtained for different eye distances to object (d), specifically for 0.4 m, 1.0 m and 6.0 m, as well as for different pupil diameters (D), specifically for 2.5 mm, 3.5 mm and 5.0 mm.

As can be seen in Figure 5, the known lens provides adequate correction for presbyopia for eye-to-object distances (d) of 0.4 m. At this distance, a change in the pupil diameter (D) only affects the contrast of the viewed image, although this variation in contrast can be considered acceptable for the normal range of pupil diameters (D) between 2.5 mm and 5.0 mm.

However, Figure 5 also shows that as the eye-to-object distance (d) increases, the image quality deteriorates, becoming more pronounced as the pupil diameter (D) decreases. Thus, at an eye-to-object distance (d) of 1.0 m, the image can only be distinguished, albeit with poor quality, for pupil diameters (D) of 3.5 mm to 5.0 mm.

Likewise, in Figure 5 it can be observed that at a distance (d) of 6.0 m the image can only be distinguished, although with very poor quality, for pupil diameters (D) of 5.0 mm, with artifacts appearing for pupil diameters (D) of 2.5 mm to 3.5 mm, becoming more noticeable the smaller the pupil diameter (D).

Figure 6 shows the polychromatic impulse response of the eye with the known presbyopia correction lens design from Figure 4, for a visible light beam consisting of wavelengths of 0.6563 μm, 0.5876 μm, and 0.4806 μm. The representation was obtained for different object distances (d) of 0.4 m, 1 m, and 6 m, as well as for different pupil diameters (D) of 2.5 mm, 3.5 mm, and 5.0 mm.

Figure 6 demonstrates not only the sensitivity of the known lens design to object distance (d) and pupil diameter (D), but also its sensitivity to variations in the visible wavelengths of the light beam, which corresponds to the appearance of chromatic aberrations. This results from the distortion present in the response with respect to a rounded point, generating rings or halos instead, as in the case of pupil diameters (D) of 2.5 mm and object distances (d) of 1.0 m and 6.0 m.

Next, in relation to the following figures, different representative examples of embodiment according to the invention are explained, corresponding to designs of optical elements in the form of contact lenses (1).

These examples demonstrate the effectiveness of the invention's designs for presbyopia correction by providing adequate sharpness and contrast of display, without artifacts or aberrations and with reduced sensitivity to the eye-to-object distance (d), i.e., the position of the object being observed, the pupil size (D) and the wavelength of light.

All visualizations of the 0.8 visual acuity optotypes and the polychromatic impulse response, as well as the representation of the angular mean value of the phase transfer function (PTF), shown in the figures, have been obtained by computational simulation.

The computer simulations were performed using Fourier optics and Fresnel propagation for the optical system consisting of the eye and ocular media. The polychromatic image was constructed using the three representative wavelengths employed in optical design: 0.4806 μm, 0.5876 μm, and 0.6563 μm. The simulations were also obtained considering refractive indices (k) of 1.4879, 1.4906, and 1.4971, corresponding to these wavelengths.

In the simulations, the chromatic dispersion of the ocular media was taken into account according to the modeling proposed by Thibos et al. in “The chromatic eye: a new reduced-eye model of ocular chromatic aberration in humans. Applied Optics” (1992).

The modeling of the neuronal transfer function proposed by Whatson et al. in “A standard model for foveal detection of spatial contrast” (2005) was also taken into account. The Stiles-Crawford effect was also included to account for the apodization of the field amplitude in the pupil plane (31) of the eye.

All simulations were obtained for the different eye-to-object distances (d), of 0.4 m, 1.0 m and 6.0 m, as well as for the different pupil diameters (D), of 2.5 mm, 3.5 mm and 5.0 mm.

Figures 7, 8, and 9A to 9C refer to a first example of an optical element design according to the invention. This design was obtained by selecting a surface topography expressed in polar coordinates as A(r, 0) = 16 ■ r 3 ■ cos(3 ■0) m.

As can be seen in Figure 7, the image sharpness of the 0.8 visual acuity optotype increases considerably compared to the image obtained by the known lens design, shown in Figure 5. The sharpness increases for both the different eye-to-object distances (d) considered, as well as for the different pupil sizes (D) considered.

Furthermore, Figure 8 shows that, compared to Figure 6, the polychromatic impulse response does not exhibit noticeable distortions such as rings or halos, corresponding to artifacts or chromatic aberrations. The disappearance of artifacts or chromatic aberrations is evident for all the eye-to-object distances (d) considered, as well as for the different pupil sizes (D) considered.

This qualitative improvement offered by the lens designs of the invention compared to known lens designs, as shown by this first design example through Figures 7 and 8, is generally present for all embodiments according to the invention, as also explained by the representative examples in the remaining figures.

The design method according to the invention uses the phase transfer function (PTF) of the ocular optical system formed by the optical element, taking into consideration an average angular value of said function for the different wavelengths considered, of 0.6563 μm, 0.5876 μm and 0.4806 μm.

According to the invention, the average angular value of the phase transfer function (PTF) for the different wavelengths, in absolute value, is compared with a maximum admissible threshold value in a maximum spatial frequency range suitable for obtaining a clear view.

The maximum permissible angular average value of the phase transfer function (PTF) is taken as n/2, preferably n/4 and more preferably n/8, for the spatial frequency range from 0 cycles/degree to 20 cycles/degree, preferably to 25 cycles/degree and more preferably to 30 cycles/degree.

Thus, for example, as shown in Figures 9A, 9B, and 9C, for eye-to-object distances (d) of 0.4 m and 1.0 m, the average angular value of the phase transfer function is less than n/8 across the entire spatial frequency range up to 30 cycles/degree. This holds true for all considered pupillary diameters (D), namely 5.0 mm (Figure 9A), 3.5 mm (Figure 9B), and 2.5 mm (Figure 9C).

Figures 10, 11, and 12A to 12C refer to a second example of an optical element design according to the invention. This design was obtained by selecting a surface topography expressed in polar coordinates as A(r,8) = 32·r 3· cos(3 ■ 0)^m.

As can be seen in Figure 10, corresponding to the optotype of visual acuity 0.8, this optical element design offers adequate visual sharpness for all eye distances to object (d) and pupil diameters (D) considered, also improving the contrast of the visualized image with respect to the design example of Figures 7, 8 and 9A to 9C.

Furthermore, Figure 11 shows that the polychromatic impulse response does not exhibit any noticeable distortions such as rings or halos, corresponding to artifacts or chromatic aberrations. The disappearance of artifacts or chromatic aberrations is evident for all the eye-to-object distances (d) considered, as well as for the different pupil sizes (D) considered.

From the comparison between the first design and the second design of the invention, it can be seen that an increase in parameter A, from 16 μm to 32 μm, with n and N fixed (n=3, N=3) allows for a certain improvement in sharpness, although it somewhat decreases the contrast of the displayed image.

The improvements introduced by this design example are reflected in the phase transfer function (PTF), which is represented in Figures 12A, 12B, and 12C for the respective pupil diameters (D) of 5.0 mm, 3.5 mm, and 2.5 mm. Compared to the previous example, this design example achieves an overall reduction in the absolute value of the average angular phase transfer function.

Thus, it can be seen that, although for the eye-to-object distance intervals (d) of 0.4 m and 1.0 m the average angular value is only less than pi/4 and up to 25 cycles/degree, overall an improvement in visual sharpness is achieved also for the eye-to-object distance interval (d) of 6.0 m, although for this eye-to-object distance (d) the average angular value of the PTF is only less than pi/2 and up to 20 cycles/degree.

Figures 13, 14, and 15A to 15C refer to a third example of an optical element design according to the invention. This design was obtained by selecting a surface topography expressed in polar coordinates as A(r, 0) = 16 ■ r 3 ■ cos(4 ■0) m.

As can be seen in Figure 13, corresponding to the optotype of visual acuity 0.8, this optical element design also offers adequate visual sharpness for all eye distances to object (d) and pupil diameters (D) considered, also improving the contrast of the visualized image with respect to the previous design examples.

Furthermore, Figure 14 shows that the polychromatic impulse response does not exhibit any noticeable distortions such as rings or halos, corresponding to artifacts or chromatic aberrations. The disappearance of artifacts or chromatic aberrations is evident for all the eye-to-object distances (d) considered, as well as for the different pupil sizes (D) considered.

Similar to the previous design examples, the improvements introduced by this design example are reflected in the phase transfer function (PTF), which is represented in Figures 15A, 15B, and 15C for the respective pupillary diameters (D) of 5.0 mm, 3.5 mm, and 2.5 mm. The phase transfer function takes a value of zero for the entire spatial frequency range up to more than 30 cycles/degree.

Typically, the property that the phase transfer function (PTF) vanishes over a whole range of spatial frequencies occurs when the value of N is an even number greater than 2, as in the present design example. In these cases, the design method is simplified, since selecting the parameters A, n, or N does not require considering a maximum angular average value of the transfer function, but only the spatial frequency up to which this value can be guaranteed to be zero.

Figures 16, 17, and 18A to 18C refer to a fourth example of an optical element design according to the invention. This design was obtained by selecting a surface topography expressed in polar coordinates as A(r,8) = 32·r 3· cos(4 ■ 0)^m.

Compared to the previous design example, the visual acuity optotype and polychromatic response representations show no significant difference in sharpness. However, a slight difference in contrast is noticeable. The phase transfer function (PTF) for this design example is zero at approximately 25 cycles/degree.

Figures 19, 20, and 21A to 21C refer to a fifth example of an optical element design according to the invention. This design was obtained by selecting a surface topography expressed in polar coordinates as A(r, 8) = 32r 4 cos(4 ■8) ^m.

Figures 22, 23, and 24A to 24C refer to a sixth example of an optical element design according to the invention. This design was obtained by selecting a surface topography expressed in polar coordinates as A(r,θ) = 48·r 4· cos(4 ■θ) ¡¿m.

Similar to the third and fourth design examples, these two design examples also provide adequate sharpness, absence of artifacts or aberrations, and display contrast. In both cases, the phase transfer function (PTF) is zero across the entire spatial frequency range up to more than 30 cycles/degree.

Figures 25, 26, and 27A to 27C refer to a seventh example of an optical element design according to the invention. This design was obtained by selecting a surface topography expressed in polar coordinates as A(r, θ) = 48 ■r 4· cos(6 ■θ)^m.

Similar to the two previous design examples, this design example also provides adequate sharpness, absence of artifacts or aberrations, and display contrast. In this case, the phase transfer function (PTF) is zeroed across the entire spatial frequency range up to more than 25 cycles/degree.

Looking at the design examples shown, the influence of the parameter N (with n and A fixed) on sharpness, absence of artifacts or aberrations, and display contrast can be observed. For example, comparing the design example in Figures 7, 8, and 9A at 9C(A(r, θ) = 16 ·r 3· cos(3 ■θ) ^m) with the design example in Figures 13, 14, and 15A at 15C(A(r, θ) = 16·r 3· cos(4 ■θ) ^m), a certain improvement in artifact reduction is observed, especially at large object distances (d) (6.0 m) and small pupil diameters (D) (2.5 mm).

Furthermore, the design examples presented demonstrate the influence of the parameter n (with N and A fixed) on sharpness, absence of artifacts or aberrations, and display contrast. For example, comparing the design example in Figures 16, 17, and 18A to 18C (A(r, θ) = 32r 3 cos(4θ) m) with the design example in Figures 19, 20, and 21A to 21C (A(r, θ) = 32r 4 cos(4θ) m), an increase in contrast is observed in the latter.

As shown through the examples presented, the optical element for presbyopia correction according to the invention is capable of providing presbyopia correction with reduced sensitivity to eye-to-object distance (d), pupil size (D), and light wavelength.

This reduced sensitivity provided by the contact lenses designed according to the invention is significantly less than that of presbyopia correction contact lenses known in the prior art, in particular those that employ spherical aberration to achieve the extension of the depth of focus.

In particular, the reduced sensitivity to the object's position makes it possible to increase the depth of focus and thus improve focus, for the entire range of distances (d), obtaining a sharp vision, without artifacts or aberrations and with adequate contrast at any distance (d).

Claims (15)

1. A design method for an optical element for presbyopia correction by depth of focus extension, comprising selecting an optical path difference (W(r,θ)) and/or a surface topography (A(r, θ)) of the optical element, expressed in polar coordinates (r,θ) as A ·r n·cos(N·θ φ) where, for any value of φ greater than or equal to 0 and less than 2n, the values of n, N and A are constants chosen from: - n greater than or equal to 3; - N greater than or equal to 3, in particular being an integer; and - A different from 0, in particular greater than 0; the value of A being at least as high as such that, taking a phase transfer function (PTF) of the ocular optical system formed by the optical element, an angular average value of said function, for the different wavelengths of a light beam with at least one visible wavelength, is in absolute value less than or equal to n/2, preferably n/4 and more preferably n/8 over the entire range of spatial frequencies from 0 cycles/degree to 20 cycles/degree, preferably to 25 cycles/degree and more preferably to 30 cycles/degree, and at least at an eye-to-object distance (d) in the range of 0.3 m to 0.4 m, preferably also 0.4 to 1.0 m and more preferably also 1.0 to 6.0 m. 2. Design method of an optical element according to claim 1, wherein the value of N is an even number. 3. A method for designing an optical element according to one of the preceding claims, wherein, starting from the chosen values of n, N, and A, N is increased, and optionally A is re-selected, to substantially reduce the occurrence of artifacts compared to the optical path difference (W(r,θ)) or the surface topography (A(r,θ)) initially selected, for said range of eye-to-object distances (d) and with respect to an optotype of 0.8 decimal visual acuity. 4. Design method of an optical element according to one of the preceding claims, wherein the value of N is less than or equal to 6. 5. A method for designing an optical element according to one of the preceding claims, wherein, starting from the chosen values of n, N, and A, n is increased, and optionally A is re-selected, to substantially increase the contrast compared to the initially selected optical path difference (W(r,θ)) or surface topography (A(r,θ)), for said eye-to-object distance range (d) and with respect to a 0.8 decimal visual acuity optotype. 6. Design method of an optical element according to one of the preceding claims, wherein the value of n is less than or equal to 4. 7. A method for designing an optical element according to one of the preceding claims, wherein the optical path difference (W(r, 0)) of the form W(r, θ) = A · rn • cos(N • θ φ) is obtained by selecting a variable refractive index function (k(r,θ)) and/or by generating diffraction in the optical element. 8. A design method for an optical element according to one of the preceding claims, wherein the condition of the angular average value of said phase transfer function (PTF) for choosing the value of A, is met for at least a pupil diameter (D) between 2 mm and up to 3.5 mm, and/or between 3.5 mm and up to 7 mm, in particular for at least a pupil diameter (D) of 2.5 mm, 3.5 mm and/or 5.0 mm. 9. A method for designing an optical element according to any of the preceding claims, wherein the surface topography (Δ(r,θ)) of the optical element is selected in the form A(r, θ) = A • r n • cos(N • θ φ) and the chosen values of n, N and A are such that: - for n equal to 3 and N equal to 3, A greater than or equal to 32 μm; for n equal to 3 and N greater than or equal to 4, A greater than or equal to 16 μm; - for n equal to 4 and N equal to 3, A greater than or equal to 64 μm; for n equal to 4 and N greater than or equal to 4, A greater than or equal to 32 μm; and - for values of n and N other than those mentioned, the minimum value of A being the one that results from interpolating between the values of n and N mentioned. 10. A method for designing an optical element according to one of the preceding claims, comprising selecting a curvature of a base surface, with respect to which the surface topography of the optical element is expressed, to further provide a correction of refractive errors. 11. Computer program for designing an optical element for presbyopia correction, comprising instructions such that, when the program is executed by a computer, the computer performs a design method for selecting an optical path difference (W(r,θ)) or a surface topography (A(r,θ)) of the optical element according to one of the preceding claims. 12. Optical element for presbyopia correction, having an optical path difference (W(r,θ)) or a surface topography (A(r,θ)) that is obtainable by a design method, or a computer program, according to one of the preceding claims. 13. Optical element for presbyopia correction according to claim 12, which is a contact lens (1) or an intraocular lens. 14. Optical element for presbyopia correction according to one of claims 12 or 13, including an intrastromal device. 15. Laser refractive surgery device, configured to emit laser pulses onto the cornea (2) to produce, by corneal carving, an optical path difference (W(r,θ)) or a surface topography (A(r,θ)) that is obtainable by a design method, or a computer program, according to any one of claims 1 to 11.