DE102023106207A1 - Ophthalmic lens with extended depth of field and method for producing a lens design - Google Patents

Abstract

An ophthalmic lens (10) with an extended depth of field is provided, wherein the ophthalmic lens (10) has a topographic surface modulation formed on a lens surface (16) relative to the base curve of the lens surface (16). The ophthalmic lens (10) is characterized in that the topographic surface modulation is based on a third-order polynomial function at least on a part of the at least one lens surface (16).

Description

Provided are an ophthalmic lens with extended depth of field, a lens design for producing an ophthalmic lens with extended depth of field, a method for producing an ophthalmic lens, a data set in the form of a computer-readable data signal, a method for generating a lens design for producing an ophthalmic lens with extended depth of field, a computer program, a computer-readable storage medium, a data signal and a data processing device. The disclosure thus lies in particular in the field of designs for ophthalmic lenses, in particular for intraocular lenses.

The optical designs of intraocular lenses (IOLs) currently available on the market range from simple refractive monofocal lenses with spherical or aspherical designs to complex diffractive multifocal lenses. Monofocal lenses have virtually no side effects but only correct the patient's distance vision, while some multifocal lenses may have undesirable properties but allow the patient to live a glasses-free life as they usually correct vision at different focal lengths.

In some cases, a compromise between spectacle independence and any side effects of IOLs may be desirable. For example, several optical lens designs have been developed to create enhanced depth of focus (EDOF) IOLs with minimal side effects that can correct patients' vision from distance to intermediate vision, enabling a spectacle-free lifestyle for most everyday tasks. With such IOLs, the patient often still needs glasses for reading. However, these IOLs have shown great promise based on patient satisfaction.

An example of an EDOF IOL is an IOL with the product name AT LARA from ZEISS.

US2020/0249501A1 describes a hybrid switchable liquid crystal lens device that uses a nanoparticle-doped liquid crystal layer and a nanoparticle-doped alignment layer. Using an applied voltage, the refractive index of the liquid crystal layer can be controlled and the focal length and optical power of the lens can be tuned and/or adjusted. In addition, this document describes a contact lens designed to influence the phase function at the front surface of the contact lens.

The WO2016/076714A1 describes an ophthalmic lens with an optical surface which has a shape according to a fourth degree polynomial, the arrangement being adapted to provide an optical function for a third degree polynomial to extend the depth of field. A further surface can have a shape according to a straight polynomial function, a spherical shape or a shape according to a combination of sphere and parabola.

The WO2017/165679A1 describes toric lenses with a freeform polynomial surface that forms a meridian band for a desired correction meridian.

The WO2017/165695A1 describes toric lenses with multiple zones, where an optical zone has a polynomial-based surface with a plurality of meridians with specific cylindrical powers.

The WO2017/165700A1 describes toric lenses with one or more angle-varying phase elements, which have diffractive and refractive structures.

Against the background of this prior art, the object of the present disclosure is to provide an ophthalmic lens and/or a method, each of which is suitable for enriching the prior art.

The problem is solved by the features of the independent claims. The subordinate claims and the dependent claims each contain optional further developments of the disclosure.

In a first aspect, an ophthalmic lens with an extended depth of field is provided, the ophthalmic lens having a topographic surface modulation formed on a lens surface relative to the base curve of the lens surface. The ophthalmic lens is characterized by characterized in that the topographic surface modulation on at least a part of the at least one lens surface is based on a third degree polynomial function.

In another aspect, a lens design is provided for the manufacture of an ophthalmic lens with extended depth of field. The lens design is characterized in that the manufacture of an ophthalmic lens according to the lens design results in an ophthalmic lens according to the disclosure.

In another aspect, a method of manufacturing an ophthalmic lens is provided, characterized in that the method manufactures the ophthalmic lens using a lens design according to the disclosure.

• (i) Eine numerische Repräsentation der offenbarungsgemäßen ophthalmischen Linse, wobei die numerische Repräsentation dazu ausgelegt ist, einer Herstellungsmaschine zur Herstellung der ophthalmischen Linse zugeführt zu werden; und
• (ii) Daten beinhaltend computerlesbare Instruktionen zum Steuern und/oder Regeln einer oder mehrerer Herstellungsmaschinen zur Herstellung einer offenbarungsgemäßen ophthalmischen Linse.

In another aspect, a data set is provided in the form of a computer-readable data signal comprising at least one type of the following data:

• (i) A numerical representation of the ophthalmic lens according to the disclosure, the numerical representation being adapted to be fed to a manufacturing machine for manufacturing the ophthalmic lens; and
• (ii) data containing computer-readable instructions for controlling and/or regulating one or more manufacturing machines for producing an ophthalmic lens according to the disclosure.

In a further aspect, a method is provided for generating a lens design for producing an ophthalmic lens with extended depth of field. The method comprises defining a base curve for a lens surface of the ophthalmic lens, as well as defining a topographic surface modulation relative to the base curve of the lens surface. The method is characterized in that the topographic surface modulation is defined relative to the base curve of the lens surface in such a way that the topographic surface modulation is based on a third degree polynomial function at least on a portion of the lens surface.

In another aspect, a computer program is provided comprising instructions which, when executed by a computer, cause the computer to perform a method according to the disclosure.

In a further aspect, a computer-readable storage medium is provided on which a computer program according to the disclosure is stored.

In another aspect, a data signal is provided which includes a computer program according to the disclosure.

In a further aspect, a data processing device is provided which is configured to carry out a method according to the disclosure. The data processing device can optionally be designed as a computer and/or server and/or smartphone and/or tablet computer. The data processing device can optionally have a processor and a memory.

An ophthalmic lens is an optical lens designed to correct a patient's vision defect. In particular, the ophthalmic lens can be an intraocular lens according to
DIN EN ISO 11979.1:2018. According to section 3.1.33 of DIN EN ISO 11979.1:2018, an intraocular lens is an ophthalmic lens that is intended for implantation in an eye. Alternatively, the ophthalmic lens can be designed as a contact lens and/or a spectacle lens. The intraocular lens can optionally have one or more haptics. According to the general understanding, a haptic is a non-optical, generally external component of an intraocular lens that is intended to hold the intraocular lens in place in the eye (see section 3.1.28 of DIN EN ISO 11979.1:2018). Optionally, the ophthalmic lens can be designed as an implantable contact lens.

The base curve of a lens surface can correspond to a surface refractive power of the lens surface. The base curve can optionally correspond to a profile of the lens surface without taking into account topographical modulations on the lens surface.

A topographic surface modulation can represent a structural change in the lens surface, so that the actual topographic profile of the lens surface deviates from the base curve. The topographic surface modulation can include local elevations and/or depressions of the lens body compared to the base curve. The topographic surface modulation can be designed in such a way that it leads to changed refractive properties of the lens surface and optionally of the ophthalmic lens. The topographic surface modulation can be designed in such a way that it leads exclusively to changed refractive properties of the lens surface and does not produce any diffractive effect.

A polynomial function is a mathematical function that has power terms with natural exponents, whereby several power terms can be added together. In a third-degree polynomial function, the highest power term has an exponent of the natural number three. The third-degree polynomial function can also have terms of lower power, i.e. two, one and/or zero. However, a third-degree polynomial function does not have a power term with an exponent greater than three that is not equal to zero.

The fact that the topographic surface modulation is based on a third-order polynomial function means that the spatial design of the topographic surface modulation at least partially or completely follows a third-order polynomial function or is otherwise at least partially determined by a third-order polynomial function. This can lead to a global tilting of the lens surface relative to the base surface. Optionally, the topographic surface modulation can be designed such that along the radial or diametrical course of the lens surface, the topographic surface modulation in cross-sectional view perpendicular to the base curve at least partially or partially corresponds to the third-order polynomial function. Optionally, the topographic surface modulation can be designed such that along a spiral course, optionally starting from the center of the topographic surface modulation and running outwards, the topographic surface modulation in cross-sectional view perpendicular to the base curve at least partially or partially corresponds to the third-order polynomial function. Optionally, the topographic surface modulation can be based on a third-order polynomial function such that a combination of the third-order polynomial function with another function, such as an apodization function and/or a rotation function, determines the design of the topographic surface modulation at least partially or in places.

The lens design can optionally be in the form of data, in particular in the form of electronically stored or storable and/or electronically readable data. The lens design can contain information that enables an ophthalmic lens to be manufactured according to the lens design. The lens design can optionally represent a “digital twin” of a physically existing ophthalmic lens.

The method for producing a lens design can optionally be designed as a computer-implemented method, i.e. one, several or all steps of the method can be carried out at least partially by a computer or a device for data processing, optionally the data processing device.

The disclosure offers the advantage that an ophthalmic lens with an extended depth of field can be provided which has a lower level of undesirable side effects than conventional EDOF lenses. In particular, intraocular lenses (IOLs) with an extended depth of field can thereby be provided which have a lower level of side effects than conventional EDOF IOLs. In addition, the disclosure offers the advantage that a large depth of field can still be provided, for example from +0.5 D to +4 D and in particular from +1.5 D or more. Optionally, this can be achieved while the side effects can be kept similarly low as with monofocal ophthalmic lenses.

In addition, the disclosure offers the advantage that the extended depth of field can be achieved with refractive means. The ophthalmic lens can thus be provided without the need for diffractive structures. This can simplify the manufacture of the ophthalmic lens and reduce manufacturing costs. In particular, this can offer the advantage that the manufacture of delicate diffractive structures, especially in edge areas of intraocular lenses, can be avoided, which can often pose a challenge in terms of manufacturability.

Furthermore, the disclosure offers the advantage that ophthalmic lenses can be provided which have a high degree of optical sharpness and contrast sensitivity.

In addition, the disclosure offers the advantage that undesirable artifacts can be avoided or reduced when imaging through an ophthalmic lens. In particular, the disclosure offers the advantage that, in contrast to ophthalmic lenses with diffractive structures, undesirable foci due to further orders of diffraction can be avoided. Accordingly, an ophthalmic lens can be provided which enables higher visual acuity than conventional aspheric lenses. In particular, the disclosure can make it possible to provide maximum visual acuity which can be comparable to the visual acuity provided by a monofocal lens.

Optionally, the ophthalmic lens has a topographic surface modulation on only one lens surface. This can be, for example, the lens surface on the front or on the back, i.e. on the side facing away from or facing the retina of the eye. Optionally, the ophthalmic lens has a topographic surface modulation on both lens surfaces, for example on the front and on the back. The two topographic surface modulations can be identical, similar or different from one another.

Optionally, topographic surface modulation is not rotationally symmetrical. This can be because a third-degree polynomial function is not symmetrical to the vertical axis through the zero point, but can have a change of sign. In particular, the topographic surface modulation can be designed such that a first part of the lens surface is raised relative to the base surface by the topographic surface modulation, while another part of the lens surface is lowered relative to the base surface by the topographic surface modulation. Optionally, the topographic surface modulation can be designed such that the lens surface is tilted relative to the base surface. This can be advantageous for expanding the depth of field. In particular, this can be advantageous in that an expansion of the depth of field can be achieved with particularly few side effects.

wobei x und y kartesischen Koordinaten einer Linsenebene entsprechen, und wobei zumindest a ≠ 0 und/oder d ≠ 0 gilt. Der Koordinatenursprung kann dabei im Zentrum der Linsenoberfläche liegen oder in einem Abstand von 0,5 mm oder weniger vom Zentrum der Linsenoberfläche entfernt. Das Zentrum der Linsenoberfläche kann auf der optischen Achse der ophthalmischen Linse liegen.The polynomial function can optionally correspond to the following mathematical relationship, here for example of third degree: $$P\left(x,y\right)=a{x}^3+b{x}^{2}y+\mathrm{<figure-callout\; id="2"\; label="c\; x\; y"\; filenames="DE102023106207A1\_0016.png"\; state="\{\{state\}\}">c</figure-callout>}x{y}^{}{}^2+d{y}^3$$

where x and y correspond to Cartesian coordinates of a lens plane, and where at least a ≠ 0 and/or d ≠ 0. The coordinate origin can be in the center of the lens surface or at a distance of 0.5 mm or less from the center of the lens surface. The center of the lens surface can be on the optical axis of the ophthalmic lens.

Optionally, the polynomial function can have a further constant term which depends neither on x nor on y. In the unit mm ^-2 , the following can apply to the parameters a and d: -0.5 < a < 0.5 and/or -0.5 < d < 0.5. These parameter ranges can be particularly suitable for providing an ophthalmic lens, in particular an IOL, with a suitable depth of field. Optionally, the parameters can each lie in a range between -0.1 and 0.1.

The following can optionally apply to the parameters b and/or c: b = 0 and/or c = 0. This means that the mixed terms, which depend on both x and y, are equal to zero and therefore do not contribute to the polynomial function. This means that the third-order polynomial function can be kept particularly simple. However, third-order polynomial functions are also optionally possible in which the parameters b and/or c are not equal to zero and contribute accordingly to the polynomial function.

The shape of the base curve of the lens surface can optionally have one or more of the following properties: rotationally symmetrical, non-rotationally symmetrical, spherical, conical, toric, biconic and aspherical. Optionally, the base curve can be determined at least partially rotationally symmetrically by polynomial terms around the center of the lens surface. In other words, various designs of the base curve are possible, whereby the designs can be based, for example, on one or more of the geometric shapes mentioned. This offers the advantage that the choice of a shape for the base curve can offer a degree of freedom for the optimization of the ophthalmic lens.

$$Sag\left(r\right)=\frac{c_B\left(r^2\right)}{1+\sqrt{1-\left(1+Q\right)c_B{}^2{r}^2}}$$

Optionally, the base curve of the lens surface can follow one of the following mathematical functions: $$SaG\left(r\right)=\frac{c_B\left(r^2\right)}{1+\sqrt{1-\left(1+Q\right)c_B{}^2{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="DE102023106207A1\_0016.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}}+{\displaystyle {\sum }_{i=1}^N{\alpha }_i{r}^i}$$

$$SaG\left(r\right)=\frac{c_B\left(r^2\right)}{1+\sqrt{1-\left(1+Q\right)c_B{}^2{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="DE102023106207A1\_0016.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}}$$

Where c _B is the inverse radius of curvature of the lens surface or the base surface, r is the radial coordinate and α _i is the coefficient of rotationally symmetric aspheric terms.

Optionally, the base curve of the lens surface can follow the following mathematical function: $$SaG\left(x,y\right)=\frac{c_x{x}^2+{\mathrm{<figure-callout\; id="2"\; label="c\; y\; y"\; filenames="DE102023106207A1\_0016.png"\; state="\{\{state\}\}">c</figure-callout>}}_y{y}^{}{}^2}{1+\sqrt{1-\left(1+Q_x\right)c_x{}^2{x}^2-\left(1+Q_y\right)c_y{}^2{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="DE102023106207A1\_0016.png"\; state="\{\{state\}\}">y</figure-callout>}}^2}}$$

Here, c _x and c _y represent the curvature of the lens in the meridian of the x-coordinate and y-coordinate, respectively, and Q _x and Q _y are the Konin constants in the x-coordinate and y-coordinate, respectively. In general, any toric base curve can additionally have rotationally symmetric polynomial terms.

The topographic surface modulation can optionally extend over only a part of the lens surface. Alternatively, the topographic surface modulation can optionally extend over the entire lens surface. Optionally, the topographic surface modulation can extend over at least 80% of the lens surface. Optionally, the topographic surface modulation can be limited to an area of the lens surface that is adapted to a typical pupil size. The choice of the extent of the topographic surface modulation on the lens surface can serve as a degree of freedom to adapt the topographic lens to different pupil sizes under different lighting conditions.

The polynomial function can be modified by an apodization function at least in a partial area of the topographic surface modulation. This can serve to weaken and/or modify the expression of the topographic surface modulation in some areas of the invention compared to the polynomial function. Optionally, the apodization function can be designed such that the topographic surface modulation deviates from the polynomial function in one or more areas in which the topographic surface modulation would have a particularly large amplitude or expression according to the polynomial function. Alternatively or additionally, the apodization function can be designed such that the expression of the topographic surface modulation is weakened in edge areas of the lens surface, which are typically covered by the iris of the eye. The ophthalmic lens can optionally be designed such that the polynomial function is not modified by the apodization function in a radial central area of the lens surface, and is modified by the apodization function in a radial outer area adjacent to the radial central area. Optionally, the apodization function can reduce an amplitude of the polynomial function in the radial outer region. Optionally, the apodization function can reduce the amplitude in the radial outer region to zero. The apodization function can thus offer another degree of freedom for optimizing the ophthalmic lens.

The apodization function can have a minimum radius at which it begins and/or a maximum radius at which it ends. The minimum radius can be zero and accordingly the apodization function can begin in the center of the lens surface. Alternatively, the minimum radius can be greater than zero and accordingly the apodization function does not necessarily have to begin in the center of the lens surface. For example, the minimum radius can be 0.5 mm. The maximum radius can optionally extend to the edge of the lens surface. Optionally, however, the maximum radius can be smaller than the radius of the lens surface and accordingly the apodization function can already end within the lens surface. Optionally, the maximum radius of the apodization function can be 3 mm. The apodization function can optionally be used to reduce the polynomial function at the edges so that the apodization does not end at the edge of the lens surface. but further inside the lens surface. However, the apodization function does not necessarily reduce the polynomial modulation to zero.

The apodization function may optionally correspond to at least one of the following functions: a step function, a linear function, a quadratic function, an exponential function, and/or a parabolic function.

The topographic surface modulation can correspond to the polynomial function at least in a partial area of the lens surface. In other words, the topographic surface modulation can be determined exclusively by the polynomial function and/or follow the polynomial function at least in a partial area of the lens surface or on the entire lens surface.

The topographic surface modulation can optionally be based on the third degree polynomial function on at least part of the lens surface in such a way that the topographic surface modulation corresponds to the third degree polynomial function modified with a rotation function. The rotation function can rotate the polynomial function locally by a predetermined angle of rotation in the circumferential direction of the lens surface depending on the radial position on the lens surface. The circumferential direction can be perpendicular to an optical axis of the ophthalmic lens. In other words, the rotation function can be designed in such a way that these different radial sections of the topographic surface modulation based on the polynomial function rotate in the circumferential direction of the lens surface by an angle of rotation that depends on the radial position. The radial sections can represent discrete sections that can be demarcated from one another or can be infinitesimally small and represent a continuum. In other words, the rotation function can be designed in such a way that different radial components of the polynomial function underlying the topographic surface modulation are rotated to different extents in the circumferential direction. This may provide the advantage that the rotational asymmetry of the topographic surface modulation can be reduced. In other words, this may provide the advantage that a degree of radial isotropy of the topographic surface modulation from a center of the lens surface can be increased. This may optionally further improve mechanical and/or optical properties of the ophthalmic lens.

The rotation function can optionally be designed such that the dependence of the predetermined angle of rotation on the radial position on the lens surface is linear or quadratic or polynomial or hyperbolic or exponential or step-like. This can offer a further degree of freedom for optimizing the ophthalmic lens. The angle of rotation can be approximately in a range from 0° to 360°. Optionally, the angle of rotation can extend from the center of the lens surface to the edge of the lens surface in a range from 0° to 360°.

The dependence of the predetermined angle of rotation on the radial position on the lens surface according to the rotation function can optionally extend over the entire radial region of the lens surface on which the topographic surface modulation is formed, or can be limited to only a partial region of the topographic surface modulation or the lens surface. In particular, the rotation function can be combined with an apodization function. This can offer further degrees of freedom in the design of the ophthalmic lens.

Optionally, the course of a height profile at the edge of the ophthalmic lens follows the course of the third degree polynomial function even if the polynomial function has been modified with a rotation function. The height profile at the edge of the ophthalmic lens, i.e. at the radially outer end of the ophthalmic lens, can remain the same even after modification of the polynomial function with a rotation function.

When the third degree polynomial function is modified with a rotation function, the topographic surface modulation can still correspond to the third degree polynomial function. This can be particularly evident when the surface profile is displayed in polar coordinates or in coordinates that have been transformed with the rotation function, rather than in the Cartesian coordinates x and y.

wobei R_max der maximale Radius des Anwendungsbereichs der Drehfunktion und φ der Winkel ist, welcher eine von der Drehfunktion in die Polynomfunktion induzierte „Spirale“ charakterisiert. Optional kann der maximale Radius bei einer IOL 3 mm betragen.The rotation function can optionally be designed as follows: $$\tau ={\left(\frac{x^2+y^2}{R_{max}}\right)}^5\phi$$

where R _max is the maximum radius of the application area of the rotation function and φ is the angle that characterizes a "spiral" induced by the rotation function in the polynomial function. Optionally, the maximum radius for an IOL can be 3 mm.

The rotation function can optionally have a minimum radius. This means that the rotation function does not start in the center of the lens, but only affects the polynomial function from a minimum radius greater than zero. Optionally, the minimum radius for an IOL can be 0.5 mm.

The method for generating a lens design for producing an ophthalmic lens with an extended depth of field can further comprise modifying the polynomial function at least in a partial area of the topographic surface modulation by means of an apodization function. Alternatively or additionally, the method for generating a lens design for producing an ophthalmic lens with an extended depth of field can further comprise modifying the third-order polynomial function with a rotation function such that the rotation function locally rotates the polynomial function by a predetermined angle of rotation in the circumferential direction of the ophthalmic lens depending on the radial position on the lens surface. This can offer further degrees of freedom for generating the lens design and in particular facilitate the generation of a lens design with an extended depth of field and few side effects.

The computer-readable storage medium can be any digital data storage device, such as a USB stick, a hard drive, a CD-ROM, an SD card, or an SSD card. The computer-readable storage medium can be readable over a network. Optionally, the computer-readable storage medium can form part of a server that provides data as a cloud server.

All disclosures and explanations relating to an ophthalmic lens are to be regarded as equally disclosed for all other disclosure subjects and vice versa, i.e. in particular for a lens design, a method for producing an ophthalmic lens, a data set in the form of a computer-readable data signal, a method for generating a lens design for producing an ophthalmic lens with extended depth of field, a computer program, a computer-readable storage medium, a data signal and a data processing device.

The features and embodiments mentioned above and explained below are not only to be regarded as disclosed in the respective explicitly mentioned combinations, but are also included in the disclosure content in other technically meaningful combinations and embodiments.

Further details and advantages will now be explained in more detail using the following examples and optional embodiments with reference to the figures.

• 1 einer schematischen Darstellung eine ophthalmische Linse mit erweiterter Schärfentiefe gemäß einer optionalen Ausführungsform;
• 2A in einer schematischen Darstellung eine beispielhafte Visualisierung der Form einer Linsenoberfläche mit einer konischen Basiskurve und einer topographischen Oberflächenmodulation in Form einer Polynomfunktion dritten Grades;
• 2B zeigt schematisch eine Apodisationsfunktion gemäß einer optionalen Ausführungsform;
• 3A und 3B einen Vergleich einer topographischen Oberflächenmodifikation gemäß einer optionalen Ausführungsform ohne und mit Modifikation durch eine Drehfunktion;
• 4 Modulationstransferfunktionen einer ophthalmischen Linse gemäß einer optionalen Ausführungsform;
• 5 eine Defokuskurve der Sehschärfe.
• 6 die Punktspreizfunktion einer ophthalmischen Linse gemäß einer optionalen Ausführungsform;
• 7 Bildschärfe einer IOL gemäß einer optionalen Ausführungsform;
• 8 schematisch ein Verfahren zur Herstellung einer ophthalmischen Linse gemäß einer optionalen Ausführungsform;
• 9 ein Verfahren zur Erzeugung eines Linsendesigns für die Herstellung einer ophthalmischen Linse mit erweiterter Schärfentiefe gemäß einer optionalen Ausführungsform;
• 10 schematisch eine Datenverarbeitungsvorrichtung gemäß einer optionalen Ausführungsform.

They show:

• 1 a schematic representation of an ophthalmic lens with extended depth of field according to an optional embodiment;
• 2A in a schematic representation an exemplary visualization of the shape of a lens surface with a conical base curve and a topographic surface modulation in the form of a third degree polynomial function;
• 2B schematically shows an apodization function according to an optional embodiment;
• 3A and 3B a comparison of a topographical surface modification according to an optional embodiment without and with modification by a rotation function;
• 4 Modulation transfer functions of an ophthalmic lens according to an optional embodiment;
• 5 a defocus curve of visual acuity.
• 6 the point spread function of an ophthalmic lens according to an optional embodiment;
• 7 Image sharpness of an IOL according to an optional embodiment;
• 8 schematically shows a method for producing an ophthalmic lens according to an optional embodiment;
• 9 a method of generating a lens design for producing an extended depth of field ophthalmic lens according to an optional embodiment;
• 10 schematically shows a data processing device according to an optional embodiment.

In the following figures, identical or similar elements in the various embodiments are designated by identical reference numerals for the sake of simplicity.

1 shows a schematic representation of an ophthalmic lens 10 with an extended depth of field according to an optional embodiment. The ophthalmic lens 10 is designed as an intraocular lens (IOL) which has a lens body 12 and two haptics 14. According to the embodiment shown, the lens body has a lens surface on the front and on the back.

According to the optional embodiment explained, the ophthalmic lens 10 has a topographic surface modulation formed on a lens surface relative to the base curve of the lens surface (see, for example, 2A , 2B and 3A) The ophthalmic lens 10 is characterized in that the topographic surface modulation on at least a part of the at least one lens surface is based on a third degree polynomial function.

The topographic surface modulation can be non-rotationally symmetric.

wobei x und y kartesischen Koordinaten einer Linsenebene entsprechen, und wobei zumindest a ≠ 0 und/oder d ≠ 0 gilt. In der Einheit mm^-2 kann für die Parameter a und d gelten: -0,5 < a < 0,5 und/oder -0,5 < d < 0,5. Für die Parameter b und/oder c kann gelten: b = 0 und/oder c = 0The third degree polynomial function can correspond to the following mathematical relationship: $$P\left(x,y\right)=a{x}^3+b{x}^{2}y+\mathrm{<figure-callout\; id="2"\; label="c\; x\; y"\; filenames="DE102023106207A1\_0016.png"\; state="\{\{state\}\}">c</figure-callout>}x{y}^{}{}^2+d{y}^3$$

where x and y correspond to Cartesian coordinates of a lens plane, and where at least a ≠ 0 and/or d ≠ 0 applies. In the unit mm ^-2, the following applies to the parameters a and d: -0.5 < a < 0.5 and/or -0.5 < d < 0.5. The following applies to the parameters b and/or c: b = 0 and/or c = 0

A shape of the base curve of the lens surface can be rotationally symmetrical and/or non-rotationally symmetrical and/or spherical and/or conical and/or toric and/or biconic and/or aspherical.

The topographical surface modulation may extend over a portion of the lens surface. In particular, the topographical surface modulation may extend over at least 80% of the lens surface.

The polynomial function can be modified by an apodization function at least in a partial area of the topographic surface modulation. In particular, the polynomial function can not be modified by the apodization function in a radial central area of the lens surface and can be modified by the apodization function in a radial outer area adjacent to the radial central area. The apodization function can optionally reduce an amplitude of the polynomial function in the radial outer area. Optionally, the apodization function can reduce the amplitude in the radial outer area to zero. The apodization function can optionally correspond to at least one of the following functions: a step function, a linear function, a quadratic function, an exponential function, and/or a parabolic function.

The topographic surface modulation can correspond to the polynomial function at least in a partial area of the lens surface.

The topographic surface modulation may be based on the third degree polynomial function on at least a part of the lens surface such that the topographic surface modulation corresponds to the third degree polynomial function modified with a rotation function, wherein the rotation function locally rotates the polynomial function by a predetermined angle of rotation in the circumferential direction of the lens surface depending on the radial position on the lens surface.

The rotation function can be designed such that the dependence of the predetermined angle of rotation on the radial position on the lens surface is linear or quadratic or polynomial or hyperbolic or exponential or step-like.

The dependence of the predetermined angle of rotation may optionally extend from the radial position on the lens surface according to the rotation function over the entire radial region of the lens surface on which the topographic surface modulation is formed, or be limited to a partial region of the topographic surface modulation or the lens surface.

An optional embodiment of an ophthalmic lens with extended depth of field is described in detail below.

According to this optional embodiment, the lens body 12 of the ophthalmic lens 10 has a lens surface with a base curve and a topographic surface modulation on the front side. The base curve has a conical shape. The topographic surface modulation follows a third degree polynomial function.

In sum, i.e. taking into account the base curve and the topographic surface modulation, the lens surface has a shape according to the following mathematical function: $$SaG\left(x,y\right)=\frac{c_B\left(x^2+y^2\right)}{1+\sqrt{1-\left(1+Q\right)c_B{}^2\left(x^2+y^2\right)}}+a{x}^3+b{x}^{2}y+\mathrm{<figure-callout\; id="2"\; label="c\; x\; y"\; filenames="DE102023106207A1\_0016.png"\; state="\{\{state\}\}">c</figure-callout>}x{y}^{}{}^2+d{y}^3$$

Where c _B is the curvature of the base surface of the lens and Q is the conical constant.

The lens surface has a global inclination or bevel, which is determined by the terms of the third-order polynomial function. The larger the terms of the third-order polynomial function, in particular the third power, the greater the inclination or bevel of the lens surface. The third-order polynomial function creates a shape of the lens surface that is not rotationally symmetrical about the optical axis of the lens body 12. Due to the asymmetric properties of the third-order polynomial function, each meridian of the ophthalmic lens has its own shape, which makes the lens body non-rotationally symmetrical and thus differs greatly from conventional designs of intraocular lenses with an extended depth of field.

An ophthalmic lens 10 according to a further optional embodiment is described below. According to this embodiment, the lens surface has a toric base curve on the front side of the lens body. The shape of the lens surface can be described by a biconical function. In total, the lens surface, ie taking into account the base curve and the topographic surface modification, has a shape that can be described by the following mathematical function: $$SaG\left(x,y\right)=\frac{c_x{x}^2+{\mathrm{<figure-callout\; id="2"\; label="c\; y\; y"\; filenames="DE102023106207A1\_0016.png"\; state="\{\{state\}\}">c</figure-callout>}}_y{y}^{}{}^2}{1+\sqrt{1-\left(1+Q_x\right)c_x{}^2{x}^2-\left(1+Q_y\right)c_y{}^2{y}^2)}}+a{x}^3+b{x}^{2}y+\mathrm{<figure-callout\; id="2"\; label="c\; x\; y"\; filenames="DE102023106207A1\_0016.png"\; state="\{\{state\}\}">c</figure-callout>}x{y}^{}{}^2+d{y}^3$$

The parameters c _x and c _y indicate the curvature of the lens surface with respect to the meridian of the x-coordinate and the y-coordinate, respectively, and Q _x and Q _y represent the conic constants for the x-coordinate and the y-coordinate, respectively.

2A shows in a schematic representation an exemplary visualization of the shape of a lens surface 16 with a conical base curve and a topographic surface modulation in the form of a third-degree polynomial function. The axes indicate the spatial coordinates x and y in millimeters. Several meridians are shown as examples, which characterize the shape of the lens surface 16. The coordinate origin is at the vertex 18 of the lens surface 16, which can coincide with the optical axis of the lens body 12. The topographic surface modulation in the form of a third-degree polynomial function creates a shape of the lens surface that is not oriented rotationally symmetrically around the optical axis.

Since the polynomial function grows rapidly with the spatial coordinates (x,y), the extent of the depth of field extension can strongly depend on the extension of the entrance pupil. In the case of ophthalmic lenses, such as IOLs or implantable contact lenses, the entrance pupil can be the object-side conjugated image of the iris of the human eye, which can represent a dynamic system that can change its diameter depending on the lighting and visibility conditions (e.g. in the case of near myosis). This can lead to the extent of the extended depth of field of such an ophthalmic lens being strongly dependent on the lighting conditions. In particular, the extension of the depth of field can increase with a larger pupil. This is not always desirable. Typically, a large extension of the depth of field is desired for near and intermediate vision, such as for near vision activities. These often take place in a well-lit environment and benefit from the physiological effect of myosis (pupil constriction), also known as the small pupil state (typically 3 mm pupil diameter for photopic conditions), while activities that take place under mesopic conditions (low light, pupil > 4.5 mm) often benefit from a low degree of extended depth of field to reduce any visual side effects.

beschrieben: $$A\left(r\right)=1f\ddot{\text{u}}r\left|r\right|<r_{min}$$

$$A\left(r\right)=S\left(r\right)f\ddot{\text{u}}r{r}_{min}<\left|r\right|<r_{max}$$

Therefore, for some optional embodiments, it may be desirable to reduce the dependence of the optical effect of the ophthalmic lens on the pupil size. This can optionally be done by an apodization function A(r), with which the third-order polynomial function or the topographic surface modulation can be modified. This modification of the third-order polynomial function by the apodization function is described below as a function of the radius $r=\sqrt{x^2+{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="DE102023106207A1\_0016.png"\; state="\{\{state\}\}">y</figure-callout>}}^2}$

described: $$A\left(r\right)=1e\ddot{\text{u}}r\left|r\right|<r_{min}$$

$$A\left(r\right)=S\left(r\right)e\ddot{\text{u}}r{r}_{min}<\left|r\right|<r_{max}$$

Where r _min and r _max represent the values of the radius at which the apodization function begins and ends. The function S(r) can take different forms, for example linear, quadratic or parabolic.

Apodization can also be useful for manufacturing purposes as it can help adjust and/or reduce a transition zone between an optical region of the lens body and the surrounding mechanical lens frame, such as an IOL.

According to a further optional embodiment, a rotation function τ(r) can be used, by means of which the third degree polynomial function or the topographic surface modulation can be modified. The rotation function can depend on the radial position on the lens surface and rotate one or more ring-shaped sections at the respective radial position of the polynomial function or the topographic surface modulation about the optical axis of the lens body. This rotation of the polynomial function or the topographic surface modulation can serve to bring the lens surface into an increasingly rotationally symmetrical configuration.

The following formula describes an example of a combination of a conical base curve and a third degree polynomial function, which leads to an overall surface shape that can be described as follows: $$SaG\left(x,y\right)=\frac{c\left(x^2+y^2\right)}{1+\sqrt{1-\left(1+Q\right)c^2\left(x^2+y^2\right)}}+a{x}^3+b{x}^{2}y+\mathrm{<figure-callout\; id="2"\; label="c\; x\; y"\; filenames="DE102023106207A1\_0016.png"\; state="\{\{state\}\}">c</figure-callout>}x{y}^{}{}^2+d{y}^3$$

$$yr\left(x,y\right)=y\text{ cos}\left(\tau \left(x,y\right)\right)+x\text{ sin}\left(\tau \left(x,y\right)\right)$$

The spatial coordinates x and y can be replaced by a coordinate transformation to a radial representation as follows: $$xr\left(x,y\right)=\text{x cos}\left(\tau \left(x,y\right)\right)-y\text{sin}\left(\tau \left(x,y\right)\right)$$

$$yr\left(x,y\right)=y\text{cos}\left(\tau \left(x,y\right)\right)+x\text{sin}\left(\tau \left(x,y\right)\right)$$

The rotation function is a peculiar function that adjusts the local angle of rotation depending on the radial position defined by the amount of x and y on the lens surface. The rotation function can, for example, be linear, polynomial or designed according to any other technically reasonable relationship.

2B shows an example of the course of a topographic surface modification along the diameter through a lens surface 16 relative to the base curve, which is not shown for better clarity. In other words, the graphs in 2B show the topographical changes brought about by the topographical surface modulation starting from the base curve. The horizontal axis shows the radius in millimeters, whereby the coordinate origin can correspond to the center of the lens surface. The vertical axis shows the topographical elevation (positive values) or depression (negative values) relative to the base curve in millimeters. Graph 200 represents a topographical modification which corresponds to a third-order polynomial function without this being modified by an apodization function. Graph 202 represents a topographical modification which corresponds to a third-order polynomial function which has been modified with an apodization function so that the expression in the radial outer area is flattened. According to the embodiment shown, the apodization function begins at a minimum radius of 0.5 mm and ends at a maximum radius of 3 mm starting from the center of the lens surface at the coordinate origin. The apodization function only modifies the polynomial function of the topographic surface modulation, but not the base area of the lens surface.

The 3A and 3B show a comparison of a topographic surface modification without ( 3A) and with modification by a rotation function ( 3B) . The false color representation shown shows in 3A that a topographical surface modulation can lead to a tilting of the surface shape relative to the base curve, whereby the surface shape is raised relative to the base curve on one side and lowered on the opposite side.

3B illustrates the effect of modifying the polynomial function by a rotation function. As indicated by the dashed arrows, the topographic surface modification is rotated to different extents in the circumferential direction depending on the radial position starting from the center of the lens surface. This creates a surface shape that is somewhat closer to a rotationally symmetrical shape than the surface shape without modification by a rotation function ( 3A) .

The ophthalmic lens 10 designed as an IOL according to 2 can have advantageous optical properties. The Through Focus Modulation Transfer Function (TF-MTF) was calculated for polychromatic light according to the luminous efficacy function to match the spectral sensitivity of human perception and thus most closely match the real conditions that patients encounter with an ophthalmic lens.

The TF-MTF for small and large pupils is in 4 , where the horizontal axis represents the refractive power in diopters and the vertical axis represents the TF-MTF in line pairs per mm (Ip/mm). Graph 402 represents the TF-MTF for a pupil diameter of 3 mm and graph 404 for a pupil diameter of 4.5 mm.

As in 4 As can be seen, the TF-MTF is characterized by slowly decreasing values around the focal point, indicating that the ophthalmic lens provides a good extended depth of field for a large diopter range, while maintaining or slowly changing contrast sensitivity over this range. Here, to influence the pupil size-dependent behavior of the extended depth of field, the polynomial function of the topographic surface modification is modified with a quadratic apodization function that smooths the contribution of the polynomial function at the edges of the lens surface.

The MTF calculations can be used to simulate the monocular visual acuity that such an IOL can offer the patient. According to the reference

Aixa Alarcon et al.: “Preclinical metrics to predict through-focus visual acuity for pseudophakic patients,” Biomed. Opt. Express 7, 1877-1888 (2016 )

The defocus curve of visual acuity can be calculated. This is shown in the example 5 The horizontal axis shows the optical power in diopters and the vertical axis the visual acuity. Graph 502 shows the case for a pupil diameter of 3 mm and graph 504 for a pupil diameter of 4.5 mm. The area which is available in the form of an extended depth of field, is indicated by arrow 506. Here, the EDOF effect, ie the extension of the depth of field up to 2 diopters, can be appreciated. In addition, the large width of the curve in the hyperopic direction shows that the visual acuity remains high even if the plane of emmetropia is not perfectly achieved after the operation, which makes the lens design very tolerant of small deviations from the perfect plane in the eye.

Graphs 502 and 504 represent calculated polychromatic visual acuity curves for photopic and mesopic conditions, respectively, with arrow 506 indicating an effective EDOF, i.e., an effective range of extended depth of field. This refers to the fact that for a patient, the useful part of the visual acuity curve lies in the myopic direction, where a diopter increase corresponds to vision at a certain distance (e.g., +1.5 D at the spectacle plane may correspond to vision at ~70 cm).

Another special feature of the ophthalmic lens according to 2A is the “triangular” point spread function (PSF) that can result from an asymmetry of the lens caused by the topographic surface modulation following a third degree polynomial function. An example of a PSF shape is given in 6 The horizontal axis shows the position in the x-direction in micrometers and the vertical axis shows the y-direction in micrometers. Here, the light focused by the ophthalmic lens is not completely concentrated in the central focal point, but is distributed asymmetrically in the x and y directions. The extent of the light distribution in the x and y directions can be controlled by the size of the polynomial coefficients a and d. The higher the value of a coefficient, the more light is distributed along this axis.

The ability of this lens design to provide high contrast sensitivity over a wide diopter range was also tested by imaging a USAFT test slide with the ophthalmic lens.

In 7 It can be seen that the image sharpness of an IOL according to an optional embodiment of 2A from the measurement points -0.82 D to +0.82 D. The upper row shows the results for a pupil diameter of 3 mm and the lower row for a pupil diameter of 4.5 mm. With a larger pupil, an effect of the PSF can be seen in the details of the optical imaging, since the resulting image through an optical system is always the product of the convolution between the imaged object and the PSF of the optical system. The effect of asymmetry can be achieved (i) by apodizing the polynomial function, (ii) by limiting the extent of the topographic surface modulation to a restricted part of the lens surface and/or (iii) by modifying it using a rotation function.

8 schematically shows a method 800 for producing an ophthalmic lens 10, characterized in that the method 800 in a step 802 produces the ophthalmic lens using a lens design according to the disclosure.

9 schematically shows a method 900 for generating a lens design for producing an ophthalmic lens 10 with extended depth of field according to an optional embodiment.

The method 900 includes, in a step 902, defining a base curve for a lens surface 16 of the ophthalmic lens 10.

In a step 904, the method 900 includes establishing a topographical surface modulation relative to the base curve of the lens surface 16.

The method 900 is characterized in that the topographic surface modulation is determined relative to the base curve of the lens surface 16 such that the topographic surface modulation is based on a third degree polynomial function on at least a portion of the lens surface 16.

Furthermore, the method 900 may comprise, in a step 906, modifying the polynomial function at least in a partial region of the topographic surface modulation by means of an apodization function.

Furthermore, the method 900 may include, in a step 908, modifying the third degree polynomial function with a rotation function such that the rotation function locally rotates the polynomial function by a predetermined angle of rotation in the circumferential direction of the ophthalmic lens depending on the radial position on the lens surface 16.

10 schematically shows a data processing device 20 according to an optional embodiment, which is configured to carry out a method for generating a lens design as described above. The data processing device can have a processor 22 and a memory 24.

List of reference symbols

10

ophthalmic lens

12

Lens body

14

Haptics

16

Lens surface

18

Vertex

20

Data processing device

22

processor

24

Storage

200

Polynomial function without modification by apodization function

202

Polynomial function modified by apodization function

402, 404

Modulation transfer function

502, 504

Visual acuity

506

EDoF, extended depth of field

800

Manufacturing process for ophthalmic lens

802

Process step

900

Method for producing a lens design

902 - 908

Process steps

QUOTES INCLUDED IN THE DESCRIPTION

This list of documents listed by the applicant was generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA accepts no liability for any errors or omissions.

Cited patent literature

• US 20200249501 A1 [0005]
• WO 2016076714 A1 [0006]
• WO 2017165679 A1 [0007]
• WO 2017165695 A1 [0008]
• WO 2017165700 A1 [0009]

Cited non-patent literature

• Aixa Alarcon et al.: “Preclinical metrics to predict through-focus visual acuity for pseudophakic patients,” Biomed. Opt. Express 7, 1877-1888 (2016 [0095]

Claims (28)

Ophthalmic lens (10) with extended depth of field, wherein the ophthalmic lens (10) has a topographic surface modulation formed on a lens surface (16) relative to the base curve of the lens surface (16), characterized in that the topographic surface modulation is based on a third degree polynomial function (200) at least on a part of the at least one lens surface (16). Ophthalmic lens (10) according to Claim 1 , where the topographic surface modulation is not rotationally symmetric. Ophthalmic lens (10) according to Claim 1 or 2 , where the polynomial function (200) corresponds to the following mathematical relationship: $$P\left(x,y\right)=a{x}^3+b{x}^{2}y+cx{y}^2+d{y}^3$$

where x and y correspond to Cartesian coordinates of a lens plane, and where at least a ≠ 0 and/or d ≠ 0. Ophthalmic lens (10) according to Claim 3 , where in the unit mm ^-2 for the parameters a and d: -0,5 < a < 0,5 and/or -0,5 < d < 0,5. Ophthalmic lens (10) according to Claim 3 or 4 , where for the parameters b and/or c: b = 0 and/or c = 0. An ophthalmic lens (10) according to any preceding claim, wherein a shape of the base curve of the lens surface has one or more of the following properties: rotationally symmetric, non-rotationally symmetric, spherical, conical, toric, biconic and aspherical. An ophthalmic lens (10) according to any preceding claim, wherein the topographical surface modulation extends over a portion of the lens surface (16). Ophthalmic lens (10) according to one of the preceding claims, wherein the topographical surface modulation extends over at least 80% of the lens surface (16). Ophthalmic lens (10) according to one of the preceding claims, wherein the polynomial function (202) is modified by an apodization function at least in a partial region of the topographic surface modulation. Ophthalmic lens (10) according to Claim 9 , wherein the polynomial function (202) is not modified by the apodization function in a radial central region of the lens surface (16) and is modified by the apodization function in a radial outer region adjacent to the radial central region. Ophthalmic lens (10) according to Claim 10 , wherein the apodization function reduces an amplitude of the polynomial function (202) in the radial outer region. Ophthalmic lens (10) according to Claim 11 , where the apodization function reduces the amplitude in the radial outer region to zero. Ophthalmic lens (10) according to one of the Claims 9 until 12 , wherein the apodization function corresponds to at least one of the following functions: a step function, a linear function, a quadratic function, an exponential function, and a parabolic function. Ophthalmic lens (10) according to one of the preceding claims, wherein the topographic surface modulation corresponds to the polynomial function at least in a partial region of the lens surface (16). Ophthalmic lens (10) according to one of the preceding claims, wherein the topographic surface modulation is such on at least a part of the lens surface (16) on the polynomial function (200, 202) of the third degree, that the topographic surface modulation corresponds to the polynomial function (200, 202) of the third degree modified with a rotation function, wherein the rotation function rotates the polynomial function (200, 202) locally by a predetermined angle of rotation in the circumferential direction of the lens surface (16) depending on the radial position on the lens surface (16). Ophthalmic lens (10) according to Claim 15 , wherein the rotation function is designed such that the dependence of the predetermined angle of rotation on the radial position on the lens surface (16) is linear or quadratic or polynomial or hyperbolic or exponential or step-like. Ophthalmic lens (10) according to Claim 15 or 16 , wherein the dependence of the predetermined angle of rotation on the radial position on the lens surface (16) according to the rotation function extends over the entire radial region of the lens surface (16) on which the topographic surface modulation is formed, or is limited to a partial region of the topographic surface modulation or the lens surface (16). Ophthalmic lens (10) according to one of the preceding claims, wherein the ophthalmic lens (10) is designed as an intraocular lens. Lens design for the manufacture of an ophthalmic lens (10) with extended depth of field, characterized in that the manufacture of an ophthalmic lens (10) according to the lens design results in an ophthalmic lens (10) according to one of the preceding claims. Method (800) for producing an ophthalmic lens (10), characterized in that the method (800) produces the ophthalmic lens (10) using a lens design according to Claim 19 produces. A data set in the form of a computer-readable data signal comprising at least one type of the following data: (i) a numerical representation of the ophthalmic lens (10) according to one of the Claims 1 until 19 , wherein the numerical representation is designed to be supplied to a manufacturing machine for producing the ophthalmic lens (10); (ii) data containing computer-readable instructions for controlling and/or regulating one or more manufacturing machines for producing an ophthalmic lens (10) according to one of the Claims 1 until 19 . Method (900) for generating a lens design for the manufacture of an ophthalmic lens (10) with extended depth of field, comprising the steps of: - defining (902) a base curve for a lens surface (16) of the ophthalmic lens (10); - defining (904) a topographic surface modulation relative to the base curve of the lens surface (16); characterized in that the defining (9040) of the topographic surface modulation relative to the base curve of the lens surface (16) is carried out in such a way that the topographic surface modulation is based on a third degree polynomial function (200) at least on a portion of the lens surface (16). Procedure (900) according to Claim 22 , further comprising: - modifying (906) the polynomial function (200, 202) at least in a partial region of the topographic surface modulation by means of an apodization function. Procedure (900) according to Claim 22 or 23 , further comprising: - modifying (908) the third degree polynomial function with a rotation function such that the rotation function locally rotates the polynomial function (200, 202) by a predetermined angle of rotation in the circumferential direction of the ophthalmic lens depending on the radial position on the lens surface (16). A computer program comprising instructions which, when executed by a computer, cause the computer to perform a method according to one of the Claims 22 until 24 to execute. Computer-readable storage medium on which a computer program according to Claim 25 is stored in memory. Data signal which a computer program according to Claim 25 contains. Data processing device (20) which is adapted to carry out a method (900) according to one of the Claims 22 until 24 to execute.

Images