WO2009040452A1

WO2009040452A1 - Monofocal ophthalmic lenses

Info

Publication number: WO2009040452A1
Application number: PCT/ES2008/000598
Authority: WO
Inventors: Daniel CRESPO VÁZQUEZ; Jose ALONSO FERNÁNDEZ; Jose Miguel Cleva Millor
Original assignee: Indizen Optical Technologies, S.L.
Priority date: 2007-09-26
Filing date: 2008-09-22
Publication date: 2009-04-02
Also published as: ES2337970B1; ES2337970A1

Abstract

The invention relates to a novel type of ophthalmic lens designed to compensate for refractive errors with at least one non-spherical surface, in which the base and the mathematical form defining the surface are selected and calculated dynamically, with all of the optical, ergonomic and aesthetic properties of the lens being balanced simultaneously and in real time in order to obtain the best balanced lens design for each user and need.

Description

MONOFOCAL OPHTHALMIC LENS.

Object of the invention,

The object of the present invention is a method of designing ophthalmic lenses, monofocal lenses of the highest quality and ophthalmic lenses for compensation of refractive errors that are achieved with said method. Background of the invention.

It is well known that ocular refractive errors are compensated by the use of ophthalmic lenses. In a first approximation, the requirement that is required of a compensatory ophthalmic lens is that its paraxial image focus coincides with the conjugate point of the retina of the ametropic eye, for a given object distance, and for a given ocular accommodation value. In order for this circumstance to be verified, - it is sufficient that the posterior frontal power of the lens, in the paraxial sense, coincide with the refractive error. of the determined patient. in the plane of the glasses. However, and given that the eye is a rotating optical system, the visual axis can rotate in the center 'of rotation of the eye, away from the optical axis of the compensating lens of the refractive error. Under this circumstance, the power of the lens ^' ceases to coincide with the paraxial value, and the refractive error is not adequately compensated. Refractive error is traditionally specified from the main curvatures of the wavefront refracted by the eye. If we consider the difference between the curvature of a parallel beam refracted by a perfect eye, and the main curvatures corresponding to the beam refracted by the ametropic eye, and we call these differences Zc ₁ and Zf ₂ , traditionally called sphere, E, a of the two curvatures and cylinder, C, to the difference between the two. The axis of the cylinder a, is defined as the direction of the main curvature defined as a sphere. The ideal power of the compensating lens can then be specified with the three figures [E, C * á \.

The obliquity of the visual axis has the consequence that the lens has a power [E + ε (u, v), (C + χ (u, v)) * (a + a (u, v))], where uyv are the horizontal and vertical angles that determine the direction of look and are shown in Figure 1, and the functions ε, χ and β, are errors in the spherical power, in the cylinder and in the direction of the axis of the cylinder, which we will call oblique errors (sphere error, cylinder error and cylinder axis error).

The traditional design of ophthalmic lenses, from the first family of lenses free of oblique cylinder error (Punktal family, 1908) has focused mainly on the reduction of the cylinder error and on the reduction of the sphere error, of secondary form This reduction of oblique power errors (not axis) has been undertaken until now for a certain value of the angle of obliqueness, since the hypothesis is accepted under which, if the oblique error is small for a certain angle of obliqueness, It is also for the rest of the field of vision. The classic form of reduction of the oblique power error consists in the use of a meniscus form factor for the compensating lens. The meniscus shape is characterized by having an external surface of positive refracting power and an internal surface, the closest to the eye, of negative refracting power. . In this way, the oblique power errors of the external and internal faces of the lens tend to compensate. However, this format is not sufficient for a good correction of the three oblique errors. Only one of the two oblique power errors can be reduced, and even the improvement is unimportant in astigmatic lenses and in medium-high positive power lenses.

On the other hand, the meniscus shape tends to produce lenses with high curvature surfaces and with greater edge thicknesses in negative lenses or greater central thicknesses in positive lenses. As a consequence, the optimal ophthalmic lens of spherical surfaces is less ergonomic, heavier and less aesthetic. Another added problem is that the reduction of oblique power errors is only applicable in a certain position of use and for a certain position of the object observed by the user. The position of use is a general denomination that encompasses all the parameters that specify the position of the lens with respect to the eye: Distance from its vertex posterior to the center of rotation V ₂ , pantoscopic angle of the lens, γ, facial angle, φ, and decentralization of its optical center with respect to the user's pupil (x _o , y _o ). These parameters are illustrated in Figure 2.

Finally, the impositions of ophthalmic lens manufacturing systems require that at least one of the two surfaces of the lens have predefined curvature values. These values form a discrete and small set of possible curvatures, which are called bases, and partly limit the freedom to produce lenses with arbitrary shapes. In the modern industry of ophthalmic lens manufacturing, positive bases are usually used, that is, semi-finished lenses with a few possible values of curvature of the external surface. Given a prescription, the inner face of a semi-finished lens is detailed to obtain, in this way, a lens with the power required by the user. The design efforts of ophthalmic lenses have focused primarily on the reduction of oblique errors for a given direction of view defined by the angles u and v. In this sense, three positions of the eye are defined in relation to the lens: In the primary position, or main gaze position, the visual axis of the eye coincides with the optical axis of the lens.

In Ia secondary position, the eye rotates a certain angle, but its short visual axis the lens in one of its principal meridians, so that, for example, if the cylinder axis is oriented at 0 ^or or 90 °, in the position secondary or u = 0 or v = 0, but not both at the same time.

In US4310225, a family of lenses is claimed in which one is chosen from a set of internal concave surfaces, separated in dioptric value by intervals of 0.50D, to achieve a reduction of oblique errors at different values of the object distance and from the distance to the center of rotation. Given the limitation imposed by manufacturing from bases, one of the most commonly used tactics consists in replacing at least one of the spherical surfaces of the lens, easy to manufacture, by an aspherical surface, more complex but offering greater degrees of freedom. The variation of the main curvatures makes it possible, in part, to compensate for the oblique power errors caused by the obliqueness. In this sense, in US5235357, ^" a type of ophthalmic lens with the external surface in the form of a conicoid is claimed, so that oblique errors (sphere error and cylinder error) are minimized for a given frontal power and for a given index of refraction.

However, spherical surfaces with revolution symmetry have clear limitations for the reduction of oblique errors in astigmatic lenses, which is why atoric type surfaces have been introduced.

In US3960442 a new type of monofocal lens is presented in which one of the two surfaces corresponds to an atoro. This generalization allows to select the base of the lens according to a criterion different from the correction of oblique errors, for example, the equalization of retinal image sizes, or to control the appearance of certain parasitic images resulting from internal reflections in the surfaces of the lens. Once the base has been selected according to any of these criteria, the oblique errors are reduced by means of the appropriate selection of the toric surface aspherization parameters. - TO -

In the US6419549 patent a complete system of calculation and manufacturing is claimed that allows to calculate and manufacture pairs of lenses with substantially the same refractive power values of the external face despite a possible anisometropia of the patient. The possibility of calculating and carving aspherical internal surfaces allows the reduction of oblique errors even when the bases of the lenses corresponding to the right eye and the left eye, as they would be manufactured independently, are significantly different.

Another alternative that facilitates the design of aspherical ophthalmic lenses is shown in patent US7111937, which claims ophthalmic lenses in which the toric surface has been replaced by a ruled surface in which the principal curvature directions are at all points substantially parallel to the directions of the X and Y coordinate axes.

In US4978211 patent ophthalmic lenses of positive power are claimed in which the sphericity of the external face allows to melt two regions continuously, a central optical region in which the patient achieves good quality of vision, with an external area of annular shape, with tangential power substantially less than in the internal zone, and that allows to obtain positive lenses of high power and still not too central thickness and lighter than the corresponding spherical lenses. In the US5825454 patent, an aspherical lens design is claimed that is tolerant to decentralization, taking into account oblique errors (astigmatism and power error) for a certain angle of obliqueness and under certain offsets

In all the previous developments, the optimization is carried out for surfaces - with a closed analytical form, either a monk card or a parametric description of the surface. Another limitation is the realization of the optimization for director rays that cut through the main sections of the lens, and for fixed oblique angles, under the hypothesis that if the oblique error is small or null for a certain degree of obliqueness, it is also for the entire visual field. In US6012813, the use of surfaces defined by splines is claimed to achieve greater flexibility in the description thereof. It is also considered the correction of oblique power errors in the so-called "tertiary position of the eye", which is that in which the main ray does not pass through the main sections of the lens. In this patent, again the objective is to reduce the oblique errors for a certain value of the obliqueness. In another design of monofocal spherical lenses (US5550600) it is proposed, only for negative lenses, an aspherical surface with revolution symmetry in which the difference between the main curvatures, which in this case coincide with the tangential and sagittal directions, grows with the radial coordinate on a central zone, decreases in an adjacent annular zone, and then grows back on the rest (periphery) of the lens. Such design allows the obtaining of good optical quality lenses in the first zone (20 mm radius) at the same time as greater flatness and lower edge thicknesses.

In another design of negative aspherical lenses (US5083859), the improvement of said lenses is considered through the use of concave aspherical surfaces that respond to a polynomial one-dimensional function in the main meridians of the lens. In oblique meridians, the surface is defined by geometric projection of the. main meridians The improvement sought is a reduction in the oblique astigmatism error along the main directions. . However, and despite all the advances mentioned above, monofocal ophthalmic lenses are still calculated with the objective of minimizing oblique power errors below a certain tolerance for a given oblique value. Normally this guarantees that said oblique power errors are also small for smaller oblique angles, but in quite a few cases, which depend on the power of the lens and the type of asphericity chosen, the oblique errors are triggered for values greater than the angle of obliquity. This results in that the power offered by the lens in said positions moves away considerably from the paraxial frontal power. Another problem associated with ophthalmic lenses is due to transverse chromatic aberration. As demonstrated in the Mercier et al reference, transverse chromatic aberration is the cause of the greater reduction in visual acuity for secondary and tertiary gaze positions. The transverse chromatic aberration is proportional to the prismatic effect produced by the lens and inversely proportional to the Abbe number of the material with which it is manufactured. Normally it is considered that the prismatic effect grows linearly with the distance to the optical axis, so that until now it has been considered that transverse chromatic aberration can only be reduced with a low dispersion material.

Finally, note that, the design of monofocal ophthalmic lenses is limited to the optimization of a surface in response to the reduction of oblique power errors leaving aspects such as the base value or good correspondence binocular out of the optimization problem, and as part of a choice that is made a priori.

Finally, the modern point-to-point carving and polishing technology allows arbitrary surfaces to be manufactured in ophthalmic lenses, both on semi-finished surfaces with a spherical or aspherical surface of predetermined characteristics, and for the manufacture of b-aspherical lenses completely free. This ability to modify in _. Each specimen of ophthalmic lens features one or both surfaces, opens the possibility to a global optimization of the ophthalmic lens. Description of the invention. The objective of the present invention is to achieve optimized monofocal ophthalmic lenses in a global way to take into account, at the same time, the optical, binocular, ergonomic and aesthetic needs of the end user. The advantage of this optimization is that once the priorities for each problem have been selected, the calculation system will find the optimum form of both surfaces, or if semi-finishes are used, (which reduces the degrees of freedom), the system determines automatic the base together with the thickness and geometry of the carving surface, so that the lens is optimal according to the selected priorities.

For this manufacturing system to be efficient, it is necessary to describe the aspherical surfaces with. functions flexible enough to allow maximum generality, but dependent on a number of parameters small enough to be able to perform the optimization calculation in real time, which is another fundamental characteristic of the design system of the present invention. The calculation system object of the present invention uses real ray tracing in a lens-eye model that reliably replicates the real lens and eye. This calculation system is essential to determine the powers that the eye really experiences in secondary and tertiary positions. For this, a specific ophthalmic lens shape with a spherical and toric surface is decided, which has the posterior frontal power necessary for the compensation of the user's refractive error. An object space is then imposed (defined by the distances to the objects observed for each direction of gaze.) Subsequently, and from said object space, the rays coming from the object space pass through the center of rotation of the eye after The refraction in the ophthalmic lens and the deformation of the wavefront associated with each of these rays is calculated. TO From this deformation, the power that the lens offers for each direction of view is determined by standard techniques. Since the refractive error of the eye is substantially constant regardless of its position, the variations in the power of the lens in the different directions of view are translated into oblique errors, both power and axis, which are thus established in all the object space. The ray tracing described allows to determine all the optical characteristics of the lens: prismatic effect and transverse chromatic aberration for each direction of gaze, dynamic and static distortion, oblique errors and even higher order aberrations. The relative position between the lens and the eye obviously influences the calculated properties. However, this position is not normally fixed, since there are two factors that tend to modify it more or less randomly: On the one hand, the deformation of the frames that hold the lenses in position due to their continued use, and on the other, the sliding of the saddle over the patient's face due to sweat or postural defects. As a consequence, the relative position between the lens and the eye is variable, and the design system proposed in the present invention takes into account said variability. For this, small variations are made of the variables that determine the position of the lens (pantoscopic, facial angles, distance from the surface posterior to the center of rotation of the eye and vertical and horizontal offsets of the lens) and the characteristics are recalculated again optical lens under design. This is equivalent to the calculation of the gradients of the optical characteristics as a function of the 5 parameters that control the position of the lens in space. It is interesting that these gradients are minimized, especially the components associated with vertical offset and the distance to the center of rotation, which are the parameters that change most easily in the daily bearing of ophthalmic lenses. Figure 3 shows the effect of the variation of the distance to the center of rotation on the oblique cylinder error

On the other hand, the thicknesses and curvatures of the lens used for the calculation described above allow determining other characteristics such as the size of the retinal image, the visual field and the possibility of generating parasitic images.

All the information obtained with the previous calculations is introduced into a merit function designed to accommodate continuous variables, discontinuous variables, and ligatures between free parameters. These ligatures are represented by prescription characteristics (posterior frontal power of the lens and prisms if were necessary) and by the priorities defined in the problem, normally expressed as inequalities: for example, that a certain optical magnitude does not exceed a certain threshold. The next step is the use of an iterative optimization algorithm. Before the first iteration, the surface description parameters that would correspond to the initial spherical and toric surface are evaluated, and in each iteration they are modified so that the ligatures are fulfilled and the merit function evolves towards the smallest possible value. In this way an optimal ophthalmic lens design is achieved, from a global point of view. Another added advantage of the proposed design system and the resulting ophthalmic lenses is that depending on the user's preferences, it is possible to obtain lenses in which the optical quality prevails over aesthetic or ergonomic aspects, or vice versa, weigh the flatness and the weight of the lenses sacrificing in part the reduction of oblique errors. The ligatures established as dimensions to the different properties of the lenses prevent that in either case solutions are obtained too curved or with too many imperfections or optical aberrations. Brief description of the figures.

Next, a series of drawings that help to better understand the invention and that expressly relate to an embodiment of said invention that is presented as a non-limiting example thereof is described very briefly.

Figure 1 shows the lens-eye system in a typical oblique tertiary type position. In this position, the main ray defined by the center of rotation of the eye and the center of the pupil, cuts the lens out of the main meridians thereof. Figure 2 shows the parameters that define the position of the lens with respect to the eye. These are the pantoscopic and facial angles, the distance from the posterior vertex of the lens to the center of rotation of the eye, and horizontal and vertical offsets.

Figure 3a shows an optimized lens [2.2 * 90], facial 10 °. The AV is greater than 0.8 in a 20 ° cone.

Figure 3b shows the way in which these benefits can be stabilized by means of the present invention, with an optimized lens [2,2x90], facial 10 °, displaced 5 mm in axial direction. The AV remains higher than 0.8 in a 20 ° cone. Figure 3c shows the variation of the performance of a PA ophthalmic lens in which the distance to the center of rotation is modified. Lens not optimized [2,2x90], facial 10 °. VA falls to 0.3 to 20 ° to the right side (nasal in the temporary 0I ₁ in the OD). At 10 °, the AV has fallen to 0.6. The variation of the performance of an ophthalmic PA lens in which the distance to the center of rotation is modified is shown in Figure 3d. Lens not optimized [2.2 * 90], facial 10 ° and axially displaced 5 mm. The AV falls to the right side, being less than 0.3 to 10 ° to the right side, the AV has fallen to 0.5.

In figures 4a (optimized power lens [-6,2x135], base 0.5) and 4b (optimized power lens [-6,2x135], base 4.25) it is shown how the present invention allows different bases to be used to equalize the sizes Retinal imaging (ophthalmic lens augmentation) even while maintaining good visual quality unlike. which occurs in the PA lenses as shown. in figures 4c (toric power lens [-6.2x135], base 0.5) and figure 4d (toric power lens [-6.2x135], base 4.25).

Figure 5a shows the visual acuity map of the optimized lens according to the present invention for which a substantial improvement is obtained with respect to a PA lens whose visual acuity map is that of Figure 5b.

Figure 6a shows the. Visual acuity map of a PA lens which, using the present invention, can be improved according to Figure 6b, further obtaining an improvement in the thickness of the lens as seen in Figure 6c.

Figure 7a shows the visual acuity map of a prescription PA lens (+2.5.1 x0) on a 8.50 base. Figure 7b shows the same lens optimized according to the present invention using a base 4.25, which eliminates a parasitic image of type 4. Figure 7c shows the map of the PA lens made in base 4.25 showing the improvement obtained by The optimized lens.

Figure 8 shows the values of the different functions in a PA lens and an optimized lens observing how the optimization process performs the overall improvement of all the visual characteristics of the lens. Figure 9 shows typical values of the object distance as a function of the vertical viewing angle. Preferred embodiment of the invention. ^'

The surfaces of the family of ophthalmic lenses object of the present invention, are chosen so that one of them is spherical and the other, in general, aspherical without revolution symmetry, or one of the surfaces is aspherical with Ia axisymmetric and other generally axisymmetric aspherical without or generally two ^surfaces' aspherical without symmetry of revolution.

In an embodiment of the present invention, without prejudice to the possibility of using other systems for representing aspherical surfaces, an alternating aspherical form is proposed. It is possible to generate an atoric surface in different ways. Specifically, if we call η yr _z a. the main radii of greater and lesser curvature at the apex of the surface, an atomic surface of type A with a ring format will be given by a Monge card of the type:

where

and where Ci and C ₂ are the asphericity coefficients of each major meridian. On a type B atoric surface with a ring format, the Monge card is given by:,

where,

Both atoric forms have their corresponding barrel version, which can be obtained by changing r-¡for r ₂ , C ₁ for C _{2 and} x for y. Each of the four atoric forms presents a different behavior outside the main meridians, in the regions where the visual axis cuts to the lens in the tertiary position. While the ring shape preserves the curvature in the meridians parallel to the maximum curvature, the barrel shape preserves the curvature in meridians parallel to the meridian of minimum curvature. On the other hand, while in the form B the aspherization affects equally all the meridians of the surface, in the form A, the asphericity in the main meridians of a point, arbitrary of the surface depends on the distance of said point to the vertex of the surface. This variability means that each type of surface has geometric, and therefore optical, slightly different properties. Thus, the A-type format is adapted better to reduce oblique errors for prescriptions without a cylinder or with a low cylinder, while form B is better adapted to the reduction of oblique errors for prescriptions with a medium-high cylinder. On the other hand, the ring shape allows a greater reduction of the power errors in surfaces of less curvature, (internal surface in positive lenses, or external surfaces in negative lenses) while the barrel shape is better adapted to the reduction of oblique errors on surfaces with greater curvature (external surface in positive lenses, or internal surfaces in negative lenses). The advantage of this embodiment is that each surface depends only on 2 parameters, which allows a rapid convergence of the optimization algorithm. Even so, the geometric variability is large by virtue of the 4 accessible surface types.

In another embodiment of the invention, the surface is described by a two-dimensional polynomial of the type: *

n, m = 0 where a _nm are coefficients, and ξ and ψ are normalized coordinates through two parameters dependent on the indices n and m. N is the maximum order of the polynomial, which can be set at a value between 4 and 6. In another embodiment of the invention the aspherical surfaces without revolution symmetry are described by a development of the type

M z = ∑χ _n P _n (x, y)

, »= 1 where χ _n are coefficients and P _n (x, y) are polynomials of x and y, of increasing order and defined in a given region Ω within which they satisfy the condition,

¡P _n (χ, y) P _m (χ, y) ώcdy = δ _nm .

Ω where M is the maximum number of polynomials to be used in development, and it is such that the order of the polynomial P _M is substantially equal to N. In either of the two previous cases, at _nm and χ _n are coefficients that define the surface and that must be obtained through the optimization process described above. The advantage of surface descriptions by polynomials is that they have more degrees of freedom, which gives more flexibility to the problem of optimization. In return, the number of coefficients on which the problem depends is made considerably greater than in the case of the four atoric surfaces of the previous embodiment, which significantly increases the calculation time. Even so, the design process described in this patent can be executed in real time, even with polynomial surfaces. In another embodiment of the present invention, oblique errors are reduced by calculating a function of merit based on the Cartesian components of the power tensioner. This tensor depends on the angular coordinates {u, v), and can be calculated by the expression:. ,

| E (u, v) + C (u, v) skí ² a (u, v) -C (M ₅ V) SUIa (M ₅ V) THING (M ₅ V) ^

^ -C (M ₅ v) without cc (u, v) eos a (u, v) E (u, v) + C (u, v) eos a (u, v) J being the main diagonal elements of this tensor the curvatures of the wavefront refracted by the lens in the x and y directions of the mobile reference system linked to the eye, and the element of the antidiagonal is the torsion of a curve x = cté, or y = cte, of said front of waves. The space of power tensors is isomorphic to SR ³ , so there is a biunivocal relationship between each value of the power tensioner and a point in three-dimensional space. The prescription of the lens is also a point of said. space and its power tensioner will be J? _obJ , so that in this preferred embodiment a standard valid in 5R ^{3 is used} as a measure of the quality of the lens for a direction of gaze. If we evaluate K gaze directions that cover the visual field more or less uniformly, the optical quality of the lens, in what refers to oblique errors, will be much better the smaller the quantity:

O ₁ - (P («/. V,) + Al)], ^{• • •}

where Wy is a positive weight that is assigned to the ith direction of view, A is the accommodation value that minimizes the functional (subject to the constraint A <= [θ, AÁ] where AA is the amplitude of accommodation of the user), K is the maximum number of look directions that are within the contour specified by the user defined normally, by the shape of the mount or manufacturing ellipse and G is a scalar function defined as:

J IMl YES IM | > (ΛC,) - ' where Nl is a 2x2 symmetric matrix, || || it is a valid norm in the space of symmetrical tensioners 2 * 2 and AV _max is a maximum value of visual acuity that depends on the user.

One of the advantages provided by this invention is that the oblique error metric presented in the previous equation treats the power as a single tensorial magnitude, instead of three independent magnitudes. In fact, the angle of minimum resolution is proportional to the norm fP _obj - (P + ^ H) II, provided that A takes the value that minimizes said norm. The visual acuity is, therefore, inversely proportional to it, as long as it does not exceed the conditions imposed by diffraction, the aberrations of the eye and the density of photoreceptors, a situation contemplated by the operator G. Thus, a choice of a suitable norm in the equation that defines Φ _x , makes, by minimizing the functional, the visual acuity that the user obtains in a certain direction of gaze is maximum. Visual acuity is the figure of merit that determines the quality of monocular vision of the patient and, therefore, a minimum value of garantiza _j guarantees the best possible quality of vision in the contour that encloses all possible directions of gaze. As a result of this improvement, and depending on the standard chosen, the design process allows for the first time to take into account the effect of the orientation of the cylinder axis, traditionally neglected in the design of ophthalmic lenses. This direction changes in tertiary gaze directions with respect to the orientation of said axis in Ia. paraxial zone The new design process allows to optimize the surfaces of the lens so that, as a whole, the visual acuity is not deteriorated by this change. Another advantage of the proposed method is that, by virtue of the operator G, the optimization process does not attempt to improve the lens to reduce the norm below 1 / AV _max , which would be an improvement that the user cannot take advantage of. This saves degrees of freedom and allows improving other characteristics of the lens through the functional ones described in subsequent embodiments of Ia. invention.

In another embodiment of the invention, the weight of the lens is calculated at each stage of the iterative process, its average curvature, and the functional is determined: Φ ₂ = W ₂ (W ₂₁ M ₁ + w ₂₂ κ), where w _∑ i and W ₂₂ are positive weights associated with the mass of the lens, and the average curvature of the lens at its vertex, K, and W ₂ is the overall weight given to the functional. A minimum value of this functional guarantees a lens of minimum weight and curvature, and therefore excellent from an ergonomic and aesthetic point of view. In another embodiment of the invention, the functional is determined

K

Φ ₃ = ∑ ^W 3, | - ?,

; = 1 where vi / _{3 /} are positive weights, \ p, \ is the module of the prismatic effect for the ith direction of view, and α is a positive constant, usually a positive integer. Since the transverse chromatic aberration is proportional to the module of the prismatic effect, and significant in the extreme part of the visual field, the weights W ₃ will have a significant value for high oblique angles, and negligible values for small oblique values. In this way the reduction of the transverse chromatic aberration does not penalize the optical quality in the central part of the field of vision.

In another embodiment of the invention, and always in each iteration of the process that seeks an optimal lens in a global sense, the functional is determined: Φ ₄ = w ₄ (Aβ-A) where Aβ is the difference in induced ophthalmic lens magnification by the prescription for the right and left eyes and Λ is the objective aniseiconia value for the patient. In general, this value will be null but there may be cases of anatomical aniseiconia that must be maintained are compensation for clinical reasons. The difference in ophthalmic lens magnification is obtained from the expression:

_{Δ /? =} __J iii l- (e _OD / 2n) tv (V _om ) l- (d / 2) tτ (Y _0β ) l- (β _{0 /} / 2π) tr (P _{o / 1} ) 1 - ^ / 2) tr (P _o; ) where eo _D , and _O ι are the central thicknesses of the corrective lenses for the right and left eyes; d is the vertex distance and P ₀ ^ _p P _0n , P ₀ ^ ₅ P ₀₇ are respectively the refracting power tensors of the external dipropia in the right and left eye lenses and the front power (objective power) of the lenses of the right and left eye. It is also possible and more convenient to calculate Aβ by means of approximate expression:

AB «^ ^{eθD? Om ~ e} or ^iVo n) ₊ í trfP _P) 2n 2

The value of Λ is determined by clinical procedures and, once known, the combined design of the lenses corresponding to the right and left eyes allows, through the minimization of the functional φ ₄ , the selection of bases and thicknesses that will guarantee a vision optimal binocular of the patient. The weight W ₄ determines Ia importance of the control of the aniseiconia induced by the pair of ophthalmic lenses versus the functional φ ₂ , which determines the flatness and the weight.

In another preferred embodiment of the invention, the functional is determined:

where w ₅ ¡, j = 1 ,,., 4 are weights assigned to different types of parasitic images, n is the index of refraction of the material and K ₁ and κ ₂ are the average curvatures at the vertices of the external surfaces and internal, respectively. The constants a _s¡ are positive numbers, preferably integers. The value of the functional

Φ ₅ becomes significantly large when the refractive powers of the lens are close to, the values that allow focusing a parasitic image, produced by reflections between the cornea and the surfaces of the lens, or reflections of the user's own face or eye in the surfaces of the lens. A small value of Φ ₅ guarantees that said images are out of focus, and therefore do not disturb the user of the ophthalmic lenses object of the present invention.

In yet another embodiment of the invention, the functional w _c is determined

Φ «=

K _n which is proportional to ^one absolute value of average radius of curvature of the inner face of the lens. Since the monofocal lenses of minimum distortion, both static and dynamic, require very high values of the internal curvature of the lens, any increase in the absolute value of said curvature results in a decrease in the distortion, either static or dynamic. The positive weight W ₆ determines the importance attached to the reduction of the distortion. As a general rule, the distortion will be greater in flat lenses than in curved lenses, so that the functional Φ ₆ evolves in the opposite direction to the form of evolution of Φ ₂ , the functional that determines the ergonomic and aesthetic factor. In general, and since the distortion is canceled in the neurological postprocessing of the Visual system, the weight W ₆ can be null, except in very specific cases in which it is of interest to minimize said aberration. In the classic lens design, and in the prior state of the art, greater attention has been typically given to the reduction of oblique errors. In the present invention, this concept is generalized and enhanced through the functional O ₁ , which not only takes into account the error in astigmatism or sphere, but also takes into account both errors together with the error in the orientation of the cylinder shaft.

In addition to this, the value of the functional Φ ₁ and Φ ₃ depends not only on the geometric parameters that define surfaces and lenses, but also depends on the distance at which the object being visualized is located.

It is well known that a lens with revolution geometry designed to be free of oblique astigmatism when distant objects are observed through it, produces such astigmatism when nearby objects are observed. In the same way, a corrected lens of power error for distant objects, has an appreciable power error while reducing astigmatism slightly when nearby objects are observed. In yet another embodiment of the invention, a functional is determined that would allow an adequate correction of the power tensor error for any direction of gaze, or what is the same, a functional is determined that allows obtaining a lens that provides maximum visual acuity for any direction of gaze, regardless of the distance at which the observed object is placed. The functional that allows this functionality is as follows:

Φ ₇ = ∑w _v G [V _obJ - (V (U ^ v _n S,) + A (S ₁ ) I)]

where s¡ is the distance at which the object is when the user looks in the ith direction, and Á (s¡) is now the accommodation value that minimizes the operator G when the user looks at an object located at a distance s, - in the ith direction. In general, we will assume that there is a function s (u, v) that determines the object distance for the direction of gaze defined by the angles u, v. This function can be completely general, but in most cases, the object distance depends fundamentally (or only) on the vertical viewing angle v. For one. general purpose lens, the positive vertical gaze angles correspond to objects at distances greater than ^L 5 or -6 meters, while the object distance begins to decrease for angles between 0 ^or -15 ° to reach the typical values from near vision, about -0.03 meters. The functions that determine the object distance with respect to the angle of view vary according to the specific use of the lens: outdoors, office, computer work, near vision, etc. A. once has Once a functional form has been chosen for the relation s (u, v), the discretization of gaze directions in ^' functional funcional ₇ leads to a corresponding discretization of the object distances, s¡ = s (u¡, Vj). The power Y (U _n V _n S ₁ ) is determined by means of the difference in tensile verges:

V (U _n V _n S _i ) = V (U _n V _n S ₁ ) 1

where V (U _n V _n S _f ) is the image tensor vergence, which is obtained as the tensor vergence of the beam refracted by the lens and evaluated in the vertex sphere. (1 / S ₁ ) I is the object vergence, which is obviously a multiple of the identity matrix.

The evaluation of the image vergence can be carried out by drawing a main beam and calculating the main curvatures of the wave fronts refracted by the two surfaces of the lens, which is achieved through the generalized Coddington equations.

To obtain an optimal lens for any distance, at least one of its two surfaces must be defined in general as a polynomial development, either in monomials or as an orthogonal polynomial development. In general, an optimal lens for any object distance will lack symmetries, such as those present in lenses for the compensation of spherical ametropias, or lenses for astigmatic ametropias with a spherical surface with revolution symmetry and another atoric surface. Because the object distance will vary for progressively more negative vertical directions of view. The correction of power error through the maximization of visual acuity will give rise to surfaces whose asphericity is changing along a vertical meridian, which eliminates any type of symmetry on the lens, similar to what occurs with progressive lenses These aspherical surfaces of general type are, therefore, the only ones that allow to manufacture lenses with maximum visual acuity for any direction of gaze and for any object distance.

Finally, we also calculate the magnitude:

which is a weighted sum of the functional gradient components φ

M squared, and that allows to determine the stability of the optical quality achieved with the minimization of φ against movements of the lens of its position relative to the eye. The weights W _8x determine the relative importance of the magnitude x. In general, the most important weights are w _Syo and w _{g /} , since the vertical runout and the vertex distance are the parameters that most easily change in the size of the glasses. This functional can be calculated from O _{1 in the} case of lenses for fixed viewing distance, or from Φ ₇ for lenses designed to be used with different object distances.

In another embodiment of the invention, any of the following two functions are determined:

6 ^' φ =] T φ _; + Φ ₈

7 = 1 for lenses designed for fixed object distance, or

7``. . . . . . .

1 = 2 ^' • for general purpose lenses, designed for variable object distances. In either of the two ways, weights have previously been selected that control each of the secondary functional φ _f , / = 1, ... 8. This functional is minimized through an algorithm that modifies in each iteration the parameters that define the ophthalmic lens, although the space of variation of these parameters is restricted to a set of ligatures,. .

where r¡¡ are the principal radii of curvature at the vertices of the external and internal faces of the lens, λ _j represents the parameters that define the asphericity of the surface or the surface itself, and _c and _6min are thicknesses center and minimum edge thickness in the lens. .

The ligatures express in a simple way non-negotiable conditions in the optimization process such as the front frontal power of the lens, in terms of sphere, cylinder and axis, the prescription prism, if any, the maximum tolerated values for visual acuity ( or for the power tensioner error standard), etc.

In Figure 4a and Figure 4b the AV is maintained higher than the unit in a 20 ° cone. However, the lens of Figure 4b, with a base 8.5 times more powerful than the first, produces an increase associated with the 8.5 times smaller form factor. In case of anisometropia, the design proposed in the present invention allows balancing the ophthalmic lens increases in both eyes without damaging the visual quality.

Figure 4c and Figure 4d show how the base 4.25 is suitable for the manufacture of monofocals with the power of this example. When moving to a base of 4.25, the AV deteriorates significantly, so that equalizing the retinal image sizes in case of anisometropia will be accompanied by a decrease in visual quality, an effect that is eliminated in the optimized lenses shown in Figures 4a and 4b.

Figure 5a shows an optimized power lens [-6.2x90]. 0.5 base. Maintains a level of visual acuity in a 30 ° cone. Figure 5b shows a toric [-6.2x90] power lens. Base 4.25 In the most suitable base for the realization of the toric lens a 30% decrease in the visual acuity at 30 ° is observed. Figure 6a shows a toric power lens [-4.0]. Figure 6b represents an optimized power lens [-4.0]. Visual acuity is maintained despite using a much flatter base than in the previous case, improving the aesthetics of the final result. Figure 6b on the left shows the profile of the optimized lens that is much thinner than the corresponding PA lens whose profile is shown on the right. Figure 7a shows a toric power lens [2.5,1x0] with base 8.25. Figure 7b shows a power lens [2.5,1x0] optimized on base 4.25. The result eliminates a parasitic image of type 4. In Figure 7c a toric power lens [2.5,1x0] is shown on a 4.25 basis. To eliminate a parasitic image of type 4 in the PA lenses it is necessary to use a flatter base: Comparing this lens with the optimized equivalent, a significant deterioration of the optical quality of the resulting toric lens is observed.

Finally, a prescription guide is developed, preferably a computer assistant, that allows the prescriber to activate or deactivate requirements intuitively to proceed with the design of a lens or pair of lenses with the desired characteristics for the user. The guide's mission is to facilitate the optimization process by deactivating incoherent requests (for example the reduction of the distortion and at the same time the reduction of the curvature of the lens) and allowing the prescriber to set minimum visual acuity levels or maximum thresholds for each one of the characteristics of the lens or pair of ophthalmic lenses that are represented in the functional Φ, a Φ ₈ .

Claims

1.- Monofocal ophthalmic lenses characterized in that the surfaces are chosen, at least one between: a spherical surface and another aspherical surface without revolution symmetry, an aspherical surface with revolution symmetry and another aspherical surface without revolution symmetry, two aspherical surfaces without symmetry of revolution.

2. Monofocal ophthalmic lenses, according to claim one, characterized in that the aspherical surfaces are represented by a toric surface with a ring format given by:

where

and where c- _\ and C ₂ are the sphericity coefficients of each main meridian, with ri also being the radius of greater curvature and r ₂ the radius of lesser curvature at the apex of the surface.

3. Monofocal ophthalmic lenses, according to claim two, characterized in that the atoric surface has its barrel version, changing ri for r ₂ and Ci for C ₂ .

4. Monofocal ophthalmic lenses, according to claim two, characterized in that the sphericity in the main meridians of an arbitrary point of the surface depends on the distance from said point to the vertex of the surface, better adapting to the reduction of oblique errors in prescriptions Without cylinder or low cylinder.

5. Monofocal ophthalmic lenses, according to claim one, characterized in that the aspherical surfaces are represented by a toric surface with a ring format given by:

where,

and where C ₁ and C ₂ are the asphericity coefficients of each main meridian, r1 being also the radius of greater curvature and r2 the radius of lesser curvature at the vertex of the surface.

6. Monofocal ophthalmic lenses, according to claim five, characterized in that the atoric surface has its barrel version, changing π for r ₂ and Ci for C ₂ .

7. Monofocal ophthalmic lenses, according to claim five, characterized in that the asferization affects all the meridians of the surface equally, adapting better to the reduction of oblique errors for prescriptions with medium-high cylinder.

8> Monofocal ophthalmic lenses, according to previous claims, characterized in that the ring format in the dull surfaces preserves the curvature in the meridians parallel to that of maximum curvature, allowing a greater reduction of the power errors in surfaces of less curvature, of the type of internal surfaces in positive lenses or internal surfaces in negative lenses, and because in addition, the barrel format in the toric surfaces preserves the curvature in meridians parallel to the meridian of minimum curvature, better adapting to the reduction of oblique errors in surfaces of greater curvature such as external surfaces in positive lenses or their internal surfaces in negative lenses.

9. Monofocal ophthalmic lenses, according to claim one, characterized in that the aspherical surface is defined by a two-dimensional polynomial of the type:

where _nm are coefficients and ξ and ψ are normalized coordinates through two parameters dependent on the indices n and m, and Λ / is the maximum order of the polynomial. ^• ,

10. Monofocal ophthalmic lenses, according to claim 9, characterized in that the maximum order of polynomial N is between 4 and 6.

11. Monofocal ophthalmic lenses, according to claim one; characterized in that aspherical surfaces without revolution symmetry are described by a development of the type:

M z = ∑x, Λ ^(χ > ^y) where χ _n are coefficients and P _n (x, y) are polynomials of x and y, of increasing order and defined in a given region Ω within which they satisfy the condition,

where M is the maximum number of polynomials to be used in development, and it is such that the order of the polynomial PM is substantially equal to N, the maximum order of the polynomial.

12.- Monofocal ophthalmic lenses, according to previous claims, characterized in that the optimization of the oblique errors of the lens is performed based on the minimization of a valid standard of the dioptric power matrix of the error G [P ₀₆ (w, v) - (P (u, v) + .4I)], where J? _ob (u, v) is the target dioptric power matrix for the direction of gaze (u, v). P (ω, v) is the dioptric power matrix of

The lens for the direction of gaze (u, v), and A is the user's accommodation.

13. Monofocal ophthalmic lenses, according to claim 12, characterized in that the norm of the dioptric power matrix of the error is inversely proportional to the user's visual acuity and takes a minimum value that is equal to the inverse of the user's visual acuity.

14. Monofocal ophthalmic lenses, according to claim 12, characterized in that T? (U, v) depends on the angular coordinates (u, v), and can be calculated by means of the expression:

_TK , _ (E (u, v) + C (u, v) sia ² a (u, v) -C (u, v) sina (u, v) thing (u, vγ \ y ~ C (u, v) sina (u, v) thing (u, v)

15. Monofocal ophthalmic lenses, according to claims 1 to 11, characterized in that the optimization of the oblique errors of the lens is performed based on the minimization of a valid standard of the dioptric power matrix of the error

G [J * _ob (u, v) - (P (u, v, $) + A (s) ϊ)], where Y _ob (u, y) is the target dioptric power matrix for the direction of gaze (u, v), where V (u, v, s) is the dioptric power matrix of the lens for the direction of view (u, v) and an object distance along said direction of view, where A (s) ) The accommodation that minimizes the previous norm for an object distance s. ι16.- Monofocal ophthalmic lenses, according to claim 15, characterized in that the norm of the dioptric power matrix of the error is inversely proportional to the user's visual acuity and takes a minimum value that is equal to the inverse of the user's visual acuity.

17. Monofocal ophthalmic lenses, according to claim 15, characterized in that T * (u, v, $) depends on the angular coordinates (u, v) and the object distance s, and is calculated by means of the expression:

s¡ 18.- Monofocal ophthalmic lenses, according to claim 15, characterized in that the visual function that is quantified is provided through the relationship between the object distance for each direction of gaze.

19.- Prescription method of monofocal ophthalmic lenses, according to claims 1 to 18, characterized in that it activates or deactivates design requirements of monofocal ophthalmic lenses.