HK1069880B - Contact or intraocular lens and method for its preparation - Google Patents
Contact or intraocular lens and method for its preparation Download PDFInfo
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- HK1069880B HK1069880B HK05102218.7A HK05102218A HK1069880B HK 1069880 B HK1069880 B HK 1069880B HK 05102218 A HK05102218 A HK 05102218A HK 1069880 B HK1069880 B HK 1069880B
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Background of the invention
The present invention relates to a contact or intraocular lens for correcting vision in an eye which may be myopic or hyperopic and/or may experience presbyopia as astigmatism.
As is known, myopia or hyperopia is usually corrected by a sphere whose center of curvature must lie on the optical axis of the lens, and the parameter used here to determine the correction to be made is the introduced spherical power, commonly known as the "sphere value".
It is known that the correction of presbyopia is advantageously obtained by a complex surface which allows to obtain progressive simultaneous vision correction, i.e. correction in which the spherical power between the centre and the periphery of the correction zone varies slightly (non-abrupt), so that a plurality of images are simultaneously formed on the retina, useful images being selected by the cortex as a result of the classification.
As is known, the correction of astigmatism is generally obtained by a toric surface, the plane of symmetry of which must be oriented according to a meridian plane of the eye to be corrected, i.e. a plane comprising the optical axis of the eye, where the parameters generally used to determine the correction to be performed include: one aspect is the angular separation between a meridian plane along which the toric surface is oriented and a reference meridian plane corresponding to the horizontal meridian plane when the lens wearer is standing, this angular difference being commonly referred to as the "axis" of correction; and, on the other hand, the introduced cylindrical power, commonly referred to as "cylinder power".
In order to maintain the correct position of the contact lens toric surface relative to the eye, it is necessary to provide means for angularly stabilizing the lens relative to the eye, in particular, a ballast prism (ballast prism) that maintains the lens position by weight; alternatively, a flange such as that disclosed in french patent No.2760853, which uses the dynamic effect of blinking to permanently hold the lens in place; it is also possible to taper or lighten the lens in the vertical direction of the eye towards the top and bottom ends, as disclosed in us patent 4,095,878; it is also possible, like the stabilizing device disclosed in us patent No.4324461, to include a ballast (ballast) and to lighten the lens on top. In all these stabilization devices, the correction part is located in the center of the lens, at the same level as the pupil of the eye to be corrected, for example, in a circle of radius 4 mm centered on the optical axis of the lens, except for the ballast prism.
Each of the above angle stabilizing means works well with the contact lenses all maintaining the correct orientation. However, although the different orientations that the lens successfully assumes may take a time average corresponding to the desired value, the magnitude of the change in orientation around this average is such as to sometimes cause a significant degradation of the optical performance.
The problem of angular stability does not arise in intraocular lenses which are manufactured in the form of an internal implant in the eye, on which retaining hooks are mounted which project radially, but which nevertheless undergo an angular displacement relative to a nominal position (nominal position) during the implant placement process.
To correct for this angular displacement, us patent No.5,570,143 proposes applying to a toric lens, which has the effect of increasing the depth of field, a technique commonly used to prevent spherical aberration, which presents an optical topography (topograph) on at least one surface, which has an effect on the depth of field with a spherical power that is high enough to correct the angular positioning pitch optical effect.
U.S. patent No.5,652,638 proposes a similar solution, but replaces the conventional technique for increasing the depth of field with concentric rings.
Us patent No.5,796,462 proposes the effect of obtaining depth of field by making one of the surfaces of the lens a toric type, where the meridian is not circular but belongs to the family of conic curves traditionally used to prevent spherical aberration. The other surface of the lens is spherical or has concentric rings.
Summary of The Invention
The present invention is designed to reduce the effects of angular displacement on a toric contact or intraocular lens by providing a corrective component having one or more novel structural features. Conventionally, the term "optical path" refers to an optical path difference introduced by a lens from a point light source at infinity on an optical axis.
In one embodiment, the lens may be configured in a "smooth non-toric" shape, and the optical path through the correcting portion of the lens, in addition to correcting astigmatism, may also correct both astigmatism and axisymmetric aberrations without abrupt surface discontinuities (i.e., "smoothness"). In another embodiment, the lens may be configured with so-called "sectors" arranged in a ring-like plane around the optical axis, such that the variation of the optical path through the correcting portion of the lens is a function of the angular separation from the reference meridian plane, and the correcting portion is divided into at least two sectors having different correction axes. In either embodiment, the corrective surface may be on one or both of the anterior or posterior surfaces of the lens, and the optical performance of the lens is increased in the case of angular displacement ("angular misalignment tolerance"). In particular, the angular misalignment tolerance is increased by at least 30% over the same situation (i.e., the same cylinder power and pupil diameter) for a standard toric lens of the same type.
The contact or intraocular lens of the present invention is best described in terms of the desired optical path through the corrective component, and those skilled in the art will appreciate the various ways in which the corrective component can be constructed to produce such an optical path. The clear profile of the specially shaped lens makes it possible to form a mold of this shape, for example. Lens processing tools may also be used. Regardless of the manner of manufacture, the present invention is intended to encompass the formation of lenses having a particular optical path.
With this object in view, the invention provides a contact or intraocular lens comprising a correcting portion for correcting possibly myopic or hyperopic and/or possibly presbyopic astigmatic vision, the lens comprising an optical axis and a reference meridian; the method is characterized in that: for astigmatism correction only, the variation of the optical path is a function of the distance from the optical axis and of the angular separation from the reference meridian, at least when this distance is 0.4 mm to 2.4 mm, according to the following equation:
δA(h，θ)＝δtoric(h，θ)+δatoric(h，θ)
in this equation:
—δtoric(h, θ) is a cylindrical optical path, which satisfies the expression δ in accordance with the parabolic approximation methodtoric(h，θ)＝C/2h2sin2(θ - φ), where φ is an axis required to correct astigmatism of the eye, expressed as an angular separation with respect to the reference meridian, where C is a cylinder power required to correct astigmatism of the eye; and
—δatoric(h, theta) is the optical path, so that when h is constant, its variation is a function of theta with a period of 2 pi, and sin2(theta-phi) is different, where the optical path additionally satisfies the condition:
Δφ’≥1.3Δφ
this inequality represents a 30% increase in the "angular misalignment tolerance", in which:
- Δ φ is the amplitude of the variable x between the ranges of variation [ -1/2 Δ φ, 1/2 Δ φ ], which is such as to confirm the following condition for any x within the interval:
MTFa[δtoric(h，θ-x)-δtoric(h，θ)]≥MTFa[0.25h2/2]
- Δ φ ' is the amplitude of the variable x between the ranges of variation [ -1/2 Δ φ ', 1/2 Δ φ ' ] which is such as to confirm the following condition for any x within that interval:
MTFa[δA(h，θ-x)-δtoric(h，θ)]≥MTFa[0.25h2/2]
the notation MTFa [ f (h, θ) ] indicates that for a light path f (h, θ), the calculated optical quality criterion (optical quality criterion) is derived from the modulation transfer function (modulation transfer function) generated by the light path, and for a predetermined pupil diameter between 4 mm and 7 mm, the MTFa [ f (h, θ) ] complies with the formula:
in this formula, v and x are polar coordinates in the angular frequency plane, v being expressed in cycles per degree and x being expressed in degrees; and wherein MTFa [ f (h, θ) ] (v, x) is a modulation transfer function of the optical path f (h, θ) according to the polar coordinates.
Once again, the term "optical path" as used above and more generally in this description refers more particularly to the difference in the optical path introduced by the lens of the light emitted by a point source located at an infinite distance on the optical axis, so that, in the sense of the present invention, the phase shift introduced by this lens is related to the optical path δ by the following relation:
_＝2πδ/λ
where λ is the wavelength of the light, negative values of δ and — correspond to the delay introduced on the light wave, and positive values indicate an advance.
Naturally, this optical path is effective because the wavelength lies in the visible range, in particular for a reference wavelength of 550 × 10-9And (4) rice.
In practice, _ (h, θ), and more generally the phase shift is either determined by interferometry or another method of measuring the optical phase shift of the light input by the lens, or may result from analysis of the wavefront emitted from the lens, which may be achieved by a Shack-Hartmann analyzer or other type of wavefront analyzer.
The modulation transfer function, MTF, can be calculated from the phase shift or optical path for a given pupil size according to well-known algorithms (see: M. born, E.wolf, optical principles, sixth edition, ed., Pergamman Press p480 (1980)). MTFa is the integral of MTF calculated according to the formula indicated above, which is a numerical criterion that makes the optical system performance characteristics well correlated with the subjective quality of the image produced by the system (reference: p.z. mouroulis, x.cheng, optics) 33: 2626-2631, 1994).
Note that equation 0.25h2A defocus of 0.25 diopter (D) corresponds to 2. The threshold for MTFa appearing above is selected as the warrantIs the value obtained in the absence of 0.25D for a pure spherical surface. It is assumed here that a 0.25D defocus for a 6 mm lens is just noticeable by the wearer (D.A. Atchison et al, subjective depth of focus of the eye, Optom. Vis. Sci.) 74: 511-520, 1997). The corresponding MTFa value is therefore selected as the minimum acceptable value. According to the invention, the threshold value allows the acceptable angular tolerance of the lens for correcting astigmatism to be determined.
It is noted that in the above-mentioned U.S. patent nos.5,570,143, 5,652,638 and 5,796,462, the proposed modifications to the classical toric lens are all related to the radial dependence of one of the surface shapes, i.e. to the variable h dependence, whereas the present invention proposes to operate on the angular dependence, either alone or in combination with the radial dependence.
More specifically, for the correction of a classical toric lens, the correction is such as to be denoted δatoricSo that when h is constant and θ is variable, δatoric(h, theta) is not constant but varies with a theta period of 360 deg. (2 pi), which is comparable to sin2(theta-phi) are different.
Thus, the non-axisymmetric component of the lens according to the invention is not completely toric.
In addition, it is noted that in each of U.S. patent nos.5,570,143, 5,652,638 and 5,796,462, the correction to a conventional toric lens is quantified based on optical power alone.
In contrast, according to the present invention, the evaluation of the correction carried out by a classical toric lens is not based on the power criterion, but on the optical quality criterion represented by MTFa.
It is noted that MTFa has so far been used in the past for optical instruments, not for eye and lens forming systems.
According to a first preferred embodiment, the term δA(h, θ) satisfies the equation:
in this equation:
-N is a set of integers; and
—βi(h) is a set of functions that satisfy the following conditions:
in this equation, N' is equal to N except 0 and 2, and hminAnd hmaxRespectively, the minimum and maximum distances with respect to the optical axis of the correction partial region for correcting astigmatism.
Note that δA(h, theta) expressed as Fourier seriesAnd (4) cosine expansion. In practice, the series is convergent, so N can be considered to be an integer from zero to several tens.
At betai(h) In the case of the following types:
it should be noted that if α isiIs constant, then the term:
and alphaiCorresponding, however, if αiNot a constant, the term corresponding to αiWeighted average over a range of h variations.
If the function delta is usedA(h, θ) the components when the index i is 0 and i is 2 collectively represent a sphero-cylindrical type correction, with the average coefficient α being other than i is 0 and i is 2iIs not 0, characterized in that the correction provided by the lens according to the invention comprises a non-axisymmetric component resulting from a correction other than that by a toric surface, but by a non-toric surface.
The sum of squares value is 0.005m-2This corresponds to a minimum threshold, which is determined experimentally, above which values are preferably used to obtain a significant optical effect.
In a preferred embodiment, the function β is a function of the shape of the structurei(h) Satisfy the equation
In this equation, αiFor i ∈ N, it is a constant coefficient.
Note that if the correction is purely spherical, then:
where P isVLIs the sphere power.
In a first preferred embodiment of this structural shape, the light path δA(h, θ) satisfies the equation:
in this equation, η is equal to ψ when θ - Φ is between 0 ° and 180 °, η is equal to ψ when θ - Φ is between 180 ° and 360 °, and c and ψ are predetermined constants. This divides the lens into 180 "sectors" with different astigmatism correction axes.
More specifically, the correcting portion of the lens according to the invention is divided into two sectors separated by a reference meridian plane, wherein the correcting axis of one sector is inclined by an angle ψ in a first direction and the correcting axis of the other sector is inclined by an angle- ψ in the other direction with respect to a conventional toric lens.
Thus, for example, if the angular displacement of the lens is 5 ° and the angle ψ is 8 ° relative to the ideal position, one sector is 3 ° from the ideal position and the other sector is 13 °.
As can be seen below, this can lead to the results: the overall image obtained on the retina by the two sectors has a better quality than that obtained by a pure toric lens with the same angular displacement, this quality being in accordance with the standard MTFa.
Note that the best results are obtained not with the exact cylinder power C, but with a slightly different power equal to C + C.
Preferably, in view of obtaining good results, the values of the constants C and ψ depending on the value of C are given by the following table, accurate to ± 0.125 diopter (D) for C + C and accurate to ± 1 ° for ψ.
| C(D) | C+c(D) | ψ |
| 3 | 3.00 | 6.3° |
| 2.5 | 2.48 | 7.6° |
| 2 | 2.04 | 9.1° |
| 1.5 | 1.49 | 12.7° |
| 1 | 1.00 | 19.1° |
This value is particularly suitable for pupil diameters of 6 mm.
Preferably, the values of the constants C and ψ depending on the value of C are given by the following table, accurate to ± 0.125 diopter (D) for C + C and to ± 1 ° for ψ, for the same reason.
| C(D) | C+c(D) | ψ |
| 3 | 2.99 | 4.7° |
| 2.5 | 2.50 | 5.7° |
| 2 | 1.98 | 7.2° |
| 1.5 | 1.49 | 9.5° |
| 1 | 0.99 | 14.4° |
This value is particularly suitable for pupil diameters of 8 mm.
It is also preferred that the constant c is equal to zero and the constant ψ has a value given by the following formula to be accurate to ± 1 ° for the same reason and in conformity with an experimentally apparent law.
In this formula, DP is the pupil diameter, expressed in millimeters (mm), ψ is expressed in degrees (°), and C is expressed in diopters (D).
In an alternative second preferred embodiment of the structural shape, the light path δA(h, θ) satisfies the equation:
in this equation, η is equal to ψ when θ - φ is between 0 ° and 90 ° and θ - φ is between 180 ° and 270 °; when theta-phi is between 90 deg. and 180 deg. and theta-phi is between 270 deg. and 360 deg., eta is equal to-psi, and c and psi are predetermined constants.
The correcting part of the lens according to the invention is therefore divided into four sectors separated by a reference meridian plane and a meridian plane perpendicular to said reference meridian plane, the correcting axes of the sectors being alternately inclined with respect to the conventional toric lens by an angle ψ in a first direction and- Ψ in the other direction.
Thus, by means of said four sectors it is possible to obtain on the retina an image of better quality than that obtained by means of a purely toric lens of the same angular displacement, which complies with the standard MTFa.
For the first preferred embodiment disclosed above, the best results are obtained not with the exact cylinder power C, but with a slightly different power equal to C + C.
It is noted that the contact lens according to this given preferred embodiment with respect to the lens according to the preferred embodiment with two opposite sectors disclosed above provides the advantage of being insensitive to decentering.
In effect the central errors are mutually compensated by the opposite sectors.
Preferably, in view of obtaining good results, the values of the constants C and ψ depending on the value of C are given by the following table, accurate to ± 0.125 diopter (D) for C + C and accurate to ± 1 ° for ψ.
| C(D) | C+c(D) | ψ(°) |
| 3 | 2.98 | 5.0 |
| 2.5 | 2.47 | 6.1 |
| 2 | 2.00 | 7.4 |
| 1.5 | 1.47 | 10.5 |
| 1 | 0.95 | 16.7 |
This value is particularly suitable for pupil diameters of 6 mm.
Preferably, for the same reason, the values of the constants C and ψ depending on the value of C are given by the following table, accurate to ± 0.125 diopter (D) for C + C and accurate to ± 1 ° for ψ.
| C(D) | C+c(D) | ψ(°) |
| 3 | 3.00 | 3.6 |
| 2.5 | 2.48 | 4.5 |
| 2 | 1.98 | 5.7 |
| 1.5 | 1.49 | 7.5 |
| 1 | 0.97 | 12.0 |
This value is particularly suitable for pupil diameters of 8 mm.
Also preferably, for the same reason and experimentally observed law, the constant c is equal to zero and the constant ψ has a value given by the following formula, accurate to ± 1 °:
in this formula, DP is the pupil diameter, expressed in millimeters (mm), ψ is expressed in degrees (°), and C is expressed in diopters (D).
In this second preferred embodiment, the term δA(h, θ) satisfies the equation:
in this equation:
e is a finite set comprising integers starting from 0; and
βi(h) is a set of functions that satisfy the following conditions:
in this equation, E' is equal to E, h except for 0 and 2minAnd hmaxRespectively, the minimum and maximum distances with respect to the optical axis of the correction segment region correcting astigmatism.
In the first preferred structure of this second embodiment, which is preferred for simplicity, each function β isi(h) All satisfy the equation:
in this equation, α for each i ∈ EiAre all constant coefficients.
The shape of this preferred configuration is clearly in accordance with an embodiment disclosed above with two or four sectors, which low-pass filters the light path, which low-pass filters only the first coefficient αiFor example, only i-10 or only i-3 is taken, and these coefficients are optimized.
Therefore, a ridge formed between sectors having different inclinations of the correction axis on the lens is prevented. This makes manufacture of the lens easier and prevents discomfort to the wearer caused by such ridges.
Preferably, the set E comprises integers from 0 to 10, based on the good results obtained with a lens according to the first preferred embodiment disclosed above having two opposite sectors; and coefficient alphaiAs a function of C, its value satisfies the inequality:
coefficient alphaIThe values of are given by the following table:
| C(D) | α0 | α1 | α2 | α3 | α4 | α5 | α6 | α7 | α8 | α9 | α10 |
| 3 | 1.521 | -0.289 | -1.450 | 0.168 | 0 | 0.040 | 0 | 0.019 | 0 | 0.011 | 0 |
| 2.5 | 1.277 | -0.284 | -1.200 | 0.168 | 0 | 0.041 | 0 | 0.019 | 0 | 0.011 | 0 |
| 2 | 1.034 | -0.299 | -0.942 | 0.165 | 0 | 0.048 | 0 | 0.022 | 0 | 0.010 | 0 |
| 1.5 | 0.775 | -0.273 | -0.661 | 0.163 | 0 | 0.040 | 0 | 0.018 | 0 | 0.011 | 0 |
| 1 | 0.522 | -0.261 | -0.383 | 0.157 | 0 | 0.038 | 0 | 0.018 | 0 | 0.010 | 0 |
this value is particularly suitable for pupil diameters of 6 mm.
Preferably, still based on the first preferred embodiment disclosed above, for the same reasons, the lens having two opposite sectors, the set E comprising integers from 0 to 10; and coefficient alphaiAs a function of C, its value satisfies the inequality:
coefficient alphaIThe values of (d) are given by the following table:
| C(D) | α0` | α1` | α2` | α3` | α4` | α5` | α6` | α7` | α8` | α9` | α10` |
| 3 | 1.502 | -0.216 | -1.465 | 0.127 | 0 | 0.031 | 0 | 0.014 | 0 | 0.008 | 0 |
| 2.5 | 1.261 | -0.218 | -1.215 | 0.126 | 0 | 0.030 | 0 | 0.014 | 0 | 0.008 | 0 |
| 2 | 1.015 | -0.214 | -0.964 | 0.127 | 0 | 0.031 | 0 | 0.014 | 0 | 0.008 | 0 |
| 1.5 | 0.766 | -0.212 | -0.695 | 0.124 | 0 | 0.030 | 0 | 0.014 | 0 | 0.008 | 0 |
| 1 | 0.516 | -0.203 | -0.425 | 0.121 | 0 | 0.030 | 0 | 0.014 | 0 | 0.008 | 0 |
this value is particularly suitable for pupil diameters of 8 mm.
It is also preferred that the set E comprises integers from 0 to 10 and the coefficient α is based on the lens with four sectors of the second preferred embodiment disclosed aboveiAs a function of C, its value satisfies the inequality:
coefficient alphaiThe values of are given by the following table:
| C(D) | α0 | α1 | α2 | α3 | α4 | α5 | α6 | α7 | α8 | α9 | α10 |
| 3 | 1.331 | 0 | -1.472 | 0 | 0.114 | 0 | 0 | 0 | 0.023 | 0 | 0 |
| 2.5 | 1.071 | 0 | -1.206 | 0 | 0.107 | 0 | 0 | 0 | 0.024 | 0 | 0 |
| 2 | 1.830 | 0 | -0.940 | 0 | 0.112 | 0 | 0 | 0 | 0.023 | 0 | 0 |
| 1.5 | 0.575 | 0 | -0.667 | 0 | 0.108 | 0 | 0 | 0 | 0.024 | 0 | 0 |
| 1 | 0.332 | 0 | -0.384 | 0 | 0.105 | 0 | 0 | 0 | 0.025 | 0 | 0 |
this value is particularly suitable for pupil diameters of 6 mm.
Preferably, still based on the second preferred embodiment disclosed above, the set E comprises integers from 0 to 10, and the coefficient α is the same for the same reason as the lens with four sectorsiAs a function of C, its value satisfies the inequality:
coefficient alpha1The values of are given by the following table:
| C(D) | α0 | α1 | α2 | α3 | α4 | α5 | α6 | α7 | α8 | α9 | α10 |
| 3 | 1.365 | 0 | -1.471 | 0 | 0.081 | 0 | 0 | 0 | 0.016 | 0 | 0 |
| 2.5 | 1.125 | 0 | -1.231 | 0 | 0.085 | 0 | 0 | 0 | 0.017 | 0 | 0 |
| 2 | 1.846 | 0 | -0.951 | 0 | 0.068 | 0 | 0 | 0 | 0.017 | 0 | 0 |
| 1.5 | 0.593 | 0 | -0.693 | 0 | 0.062 | 0 | 0 | 0 | 0.017 | 0 | 0 |
| 1 | 0.358 | 0 | -0.424 | 0 | 0.076 | 0 | 0 | 0 | 0.017 | 0 | 0 |
this value is particularly suitable for pupil diameters of 8 mm.
In the second structural shape in the second embodiment, each function βi(h) Satisfies the equation:
in this equation, j is an integer that is segmented into a functional variation of h; no matter what values i and j take, alphaijIs a predetermined constant coefficient.
Typically, each stage corresponds to an annular region in the corrective part of the lens.
The shape of the structure is well adapted to the actual situation involving changes in pupil diameter due to differences in the individual and visual environment (mainly illumination and proximity).
In the third structural shape in the second embodiment, each function βi(h) Satisfies the equation:
in which M is a predetermined integer, alphaijWhatever the values of i and j, is a predetermined constant coefficient.
The shape of the structure is similar to the previous one except for the function betai(h) Rather than varying in stages as a function of h, it varies gradually and gently.
According to a second aspect, the invention also relates to a method for manufacturing a contact or intraocular lens as described above, characterized in that it comprises:
a) the method comprises the following steps: determining an optical path that has to be introduced by the correcting portion of the lens;
b) the method comprises the following steps: selecting the shape of the posterior surface of the corrective component from a series of predetermined shapes to achieve the most comfortable feel for the wearer of the lens;
c) the method comprises the following steps: determining an anterior surface shape of the corrective component from the posterior surface shape selected in step b) and the optical path determined in step a);
d) the method comprises the following steps: the lens having the corrective portion thus determined the anterior surface and the posterior surface is manufactured.
This method of manufacturing lenses is particularly suitable for direct processing: the rear surface of the lens may have a relatively simple shape; all complex structures are transferred to the front surface, in particular so that the correcting part can introduce the required optical path, and, in the case of contact lenses, the lenses are equipped with angle-stabilizing means.
Still according to a second aspect, the invention also relates to another method for manufacturing a contact or intraocular lens as described above, characterized in that it comprises:
a) the method comprises the following steps: determining an optical path that has to be introduced by the correcting portion of the lens;
b) the method comprises the following steps: selecting a shape of the anterior surface of the orthotic shell from a series of predetermined shapes that are each axisymmetric;
c) the method comprises the following steps: determining a posterior surface shape of the corrective component from the anterior surface shape selected in step b) and the optical path determined in step a);
d) the method comprises the following steps: manufacturing the lens having the thus determined corrective part of the posterior and anterior surfaces.
This manufacturing method is particularly suitable for manufacturing the lens by molding.
In fact, since the angle maintenance means, i.e. in the case of contact lenses, the angle stabilization means are generally located on the anterior surface of the lens, it can be obtained in this embodiment that the angle maintenance means and the surface that effects the correction of astigmatism are located anterior and posterior, respectively.
This allows all axes to be achieved using the same two half molds for the same cylinder power and the same sphere power; the astigmatic axes of different values are obtained by rotation of one mold half relative to the other mold half.
Brief description of the drawings
The disclosure will now be continued by a description of preferred embodiments with reference to the accompanying drawings, which are given by way of illustration and not of limitation.
Figure 1 is a cross-sectional view of a contact lens according to the invention along its longitudinal meridian plane;
FIG. 2 is a top view of the lens;
FIG. 3 is an enlarged view of FIG. 2 showing a partial top view of the center of the lens;
figure 4 is a top view of the correcting part of the lens described in the first embodiment, which part is divided into two sectors, the correcting axis of which is inclined by a positive or negative angle ψ, respectively, with respect to the desired axis phi, for the toric type.
FIG. 5 is a graph showing how the correction axis for a toric type varies, where the angle θ - φ in degrees (°) is shown on the abscissa and the correction axis for a toric type is shown on the ordinate;
FIG. 6 is a graph (solid curve) showing how the optical path introduced by the conventional toric-type correcting section varies, and a graph (dotted curve) showing how the optical path introduced by the correcting section shown in FIG. 4 varies, where the angle θ - φ in degrees (°) is represented on the abscissa in the graph; in the case where the cylinder power required for correction is 2 diopters, it is approximated to h2The optical path of/2 is represented by the ordinate;
fig. 7 is a graph similar to fig. 6 showing the optical path obtained by low pass filtering and optimization of the optical path shown in solid line in fig. 6.
Fig. 8 is a graph showing the angular tolerance of a conventional toric lens for a cylinder power of 2 diopters and a pupil diameter of 6 mm, in which the angular displacement in degrees (°) from the desired position is shown on the abscissa of the graph and the value of MTFa is shown on the ordinate of the graph, which is obtained by calculating the difference between the optical path taken by the conventional toric lens when the angular displacement occurs and the optical path taken by the same lens whose angular position is correct (different curves will be obtained according to different cylinder powers or pupil diameters; in general, the angular misalignment tolerance of the conventional lens decreases as the cylinder power and pupil size increase).
Fig. 9 is a graph similar to fig. 8. However, the value of MTFa thereof is obtained by calculating the difference between the optical path taken by the lens having the optical path shown in fig. 7 and the optical path taken by the above-mentioned conventional toric lens when the angular position of the lens is correct (the cylinder power is 2 diopters).
FIGS. 10-13 are views similar to FIGS. 4-7, respectively, but for a second embodiment of the invention having the correcting portion divided into four sectors, the axes of which are alternately inclined by a positive or negative angle ψ; and
fig. 14 is a graph similar to fig. 7 and 13, but showing the non-toric component of the optical path shown by curves 28 and 30, respectively.
The contact lens 1 shown in the figures, in a classical manner, centered on the optical axis 2, exhibits a convex front surface 3 and a concave rear surface 4.
The rear surface is spherical and the front surface 3 presents a shape such that: when combined with the rear surface 4, the shape thereof allows the wearer to obtain the desired vision correction and also the stability of the lens with respect to the centre and rotation of the eye, through dynamic effects due to the regular blinking of the eyelids.
More specifically, the correction of vision is obtained by a portion 5 located between the optical axis 2 and the annulus at a distance of 4 mm from the optical axis, as indicated by the dashed line in fig. 2 and 3. Whereas the stabilization means comprise, in a known manner, an upper part 6 and a lower part 7 of the lens, respectively, tapering and lightening towards the edges along the vertical direction of the lens (axis of blinking of the eyelids), wherein the parts 6 and 7 cooperate with the upper and lower eyelids, respectively, so as to bring the axis 2 in line with the optical axis of the wearer's eye and the reference meridian plane 8 of said lens 1 in line with the horizontal meridian plane of the wearer's eye.
The illustrated lens is designed to achieve astigmatic correction using an axis phi, which is a correction oriented along a plane 9 (figure 3), which plane 9 has an angular separation phi with respect to a reference meridian plane 8.
Point a is any point on the front lens surface 3. The position of which is determined by the coordinates h, where h is the distance of the point a from the optical axis 2 of the lens, and theta is the angular difference between the meridian plane including the point a and said reference plane 8.
In the particular embodiment shown in figures 4-6, the correcting portion 5 is not oriented entirely along a plane 9, but is divided by this plane into two sectors 10 and 11, the axes of which are inclined in one direction and then in the other direction at an angle ψ relative to the axis phi to obtain astigmatic correction.
More specifically, in sector 10, corresponding to a point A at a range of angles θ - φ between 0 and 180, the astigmatism correction is oriented along axis φ - φ, and in sector 11, corresponding to a point A at a range of angles θ - φ between 180 and 360, the astigmatism correction is tilted along axis φ + φ, as shown by curve 12 in FIG. 5.
As is well known, according to the parabolic approximation, the optical path introduced by a conventional lens for correcting astigmatism satisfies the equation:
in this equation C is the cylinder power required to correct the astigmatism.
For those lenses having a corrective component as illustrated in fig. 4, angle phi is replaced by angle phi-psi in sector 10 and angle phi + psi in sector 11. For best possible results, for sectors 10 and 11, instead of using the cylinder degree C directly, a value C + C is used which is close to C, C being a constant.
Therefore, the optical path introduced by the correcting section 5 shown in fig. 4 satisfies the following equation:
in this equation, when θ - φ is between 0 ° and 180 °, η is equal to ψ; when θ - φ is between 180 ° and 360 °, η is equal to- ψ, which is a constant.
The curve 13, drawn as a solid line in fig. 6, represents the function 2 δtoric/h2The variation as a function of theta-phi when the cylinder power is 2 diopters, that is, in practice, it shows a function of 2sin2(theta-phi), the function also being equal to 1-cos [2 (theta-phi)]。
The dashed curve 14, representing the function 2 deltaA(h，θ)/h2That is:
when θ - Φ is between 0 ° and 180 ° (sector 10): (C + C) sin2[θ-(φ-ψ)](ii) a And
when θ - Φ is between 180 ° and 360 ° (sector 11): (C + C) sin2[θ-(φ+ψ)]，
c is zero or negligible.
Curve 14 corresponds to curve 13 shifted to the right by a value psi when theta phi is between 0 deg. and 180 deg. (sector 10), and curve 14 corresponds to curve 13 shifted to the left by a value psi when theta phi is between 180 deg. and 360 deg. (sector 11).
As described above, in this embodiment, the cylindrical power C is 2 diopters. The values of c and ψ determined by optimization are 0.04 diopters and 9.1 ° for a pupil diameter of 6 mm, respectively. This will be explained below.
It is to be noted that the optical path introduced by the correcting portion 5, as shown in fig. 4, can be expressed in the form of a fourier series expansion:
in this equation:
-N is a set of integers; and
-i for each i ∈ N is a constant coefficient.
In order to make the actual manufacture of a lens having e.g. sectors 10 and 11 easier, in particular to prevent that ridges may be present between the sectors, thus preventing discomfort to the wearer caused by the ridges, it is possible to keep only the first harmonic, e.g. incremented to i-3 or i-10, which is equivalent to low-pass filtering, and it is also possible to apply the retention factor α in the manner described below for optimum effectiAnd (6) optimizing.
By progressing from i to 10, for example, still for an eye requiring a cylinder power of 2 diopters and a pupil diameter of 6 mm, the following coefficients are obtained:
| α0 | α1 | α2 | α3 | α4 | α5 | α6 | α7 | α8 | α9 | α10 |
| 1.034 | -0.299 | -0.942 | 0.165 | 0.000 | 0.048 | 0.000 | 0.022 | 0.000 | 0.010 | 0.000 |
fig. 8 shows the calculated MTFa at an exit pupil diameter of 6 mm by curve 16, the path difference being:
δtoric(h，θ-x)-δtoric(h，θ)
wherein deltatoric(h, θ) is the optical path introduced by a conventional toric lens with a cylindrical power of 2 diopters, x is the angular displacement of the lens with respect to its ideal position, this displacement being shown on the abscissa and MTFa on the ordinate. Should be takenThis note that having different cylinder degrees or different pupil diameters will result in different curves; in general, the angular misalignment tolerance of conventional lenses decreases as the size of the cylinder and pupil increases. In this application, a "class" of lenses generally refers to lenses having the same cylinder and pupil diameter.
Thus, curve 16 represents the MTFa for each value of x for an optical system formed by a pupil diameter of 6 mm and a well-sighted eye and a hypothetical lens corresponding to the above-mentioned perturbation caused by the angular displacement of the lens.
It can be seen that in the state without perturbation (0 ° displacement), the value of MTFa is about 9.3, and starting from this value, MTFa regularly decreases with increasing angular displacement.
If the MTFa of a system composed of the same eye and a lens with spherical power around 0.25 diopter is calculated, an MTFa value of about 3.75 is obtained.
However, the perception threshold for the lens wearer to account for the optical performance degradation typically corresponds to a displacement of 0.25 diopters of spherical power.
In this embodiment, an MTFa value of 3.75 corresponds to a threshold below which the wearer of the lens begins to perceive a weakening in optical performance.
This perception threshold is shown by the horizontal line 17 shown in dashed lines in fig. 8.
It can be seen that curve 16 intersects curve 17 at an angular displacement of about 7.
This means that in the case of this embodiment (pupil diameter 6 mm, cylinder power 2 diopters), a wearer wearing a conventional lens for correcting astigmatism will begin to perceive a reduction in the optical performance of the lens when the lens is angularly displaced more than plus or minus 7 deg. from its ideal orientation.
FIG. 9, in a similar manner to FIG. 8, shows under the same conditions (e.g., using the same type)Lens) calculated MTFa, but here δtoric(h, theta-x) by deltaA(h, θ -x) instead, δA(h, θ -x) is the optical path shown in FIG. 7: the solid line depicts curve 18, representing the MTFa, and the dashed line depicts line 19, which is the same threshold as in fig. 8.
Curve 18 represents the MTFa for each x value of the optical system formed by the eye with pupil diameter of 6 mm and normal vision and the hypothetical lens. This hypothetical lens is consistent with the perturbations introduced by the fact that the conventional lens is replaced by a lens having an optical path as shown in fig. 7, while the latter lens is angularly displaced.
It can be seen that in the state without displacement (x ═ 0), MTFa has exactly the same value as the threshold shown by line 19, and a displacement of about plus or minus 2 °, beyond which the value of MTFa increases and reaches a maximum at a displacement value slightly greater than 9 °, substantially corresponding to angle ψ, and then the value of MTFa starts to regularly decrease and intersects line 19 at a displacement of about 13 °.
Although the conventional lens having an optical path as depicted by curve 13 shows an angular tolerance Δ φ of 14 and a variation range of [ -7 °,7 ° ], the lens according to the present invention, whose optical path is depicted by curve 15, shows an angular tolerance of 26 °, i.e., a variation range of [ -13 °, 13 ° ], or an increase in the amplitude of the variation range by 90%.
As indicated above, the above-mentioned coefficient α exhibiting this effectiI is incremented to 10, determined by the optimization. This consists in finding the maximum value of delta phi'.
More specifically, as described below, from some of the coefficients a previously determinedI(i increments to 10) starting with a classical optimization method such as simplex (simplex), a certain number of each coefficient varying individually is first composed to determine the partial derivative of all functions for each coefficient at the starting point, which is the direction of the bisecting half-cone change, and then the coefficients can be changed alternately until Δ is obtainedThe maximum value of phi'.
Initial coefficient alphaiI is incremented to 10, determined only by the fourier series expansion of the optical path corresponding to curve 14.
The curve itself described by the latter must be optimized beforehand in a similar way by finding (seek) the optimum operating values c and ψ.
More generally, for astigmatism corrected by a cylinder power C, the incoming optical path δ can be determined as followstoric(h, theta) angular tolerance of conventional toric lenses Δ φ and incoming optical path δA(h, θ) angular tolerance Δ φ' of a lens according to the invention:
Δ φ is the magnitude of the change of variable x in the range [ -1/2 Δ φ, 1/2 Δ φ ], which is a condition that is warranted for x taking any value in this interval:
- Δ φ ' is the magnitude of the variation of the variable x in the range [ -1/2 Δ φ ', 1/2 Δ φ ' ] which is warranted for x taking any value in this interval:
by optimizing the diameter of the pupil by delta phi' when the correcting part 5 of the lens is in the position shown in fig. 4, the following results can be obtained in terms of cylinder power for a pupil diameter of 6 mm:
| (D) | Δφ(°) | Δφ’(°) | C+c(D) | ψ(°) |
| 3 | 9.4 | 17.7 | 3.00 | 6.3 |
| 2.5 | 11.3 | 21.2 | 2.48 | 7.6 |
| 2 | 14.0 | 26.0 | 2.04 | 9.1 |
| 1.5 | 18.8 | 35.6 | 1.49 | 12.7 |
| 1 | 28.2 | 54.0 | 1.00 | 19.1 |
similarly, for a pupil diameter of 8 mm, the following values can be obtained:
| C(D) | Δφ(°) | Δφ’(°) | C+c(D) | ψ(°) |
| 3 | 7.2 | 13.4 | 2.99 | 4.7 |
| 2.5 | 8.5 | 16.2 | 2.50 | 5.7 |
| 2 | 10.6 | 20.2 | 1.98 | 7.2 |
| 1.5 | 14.0 | 27.0 | 1.49 | 9.5 |
| 1 | 21.1 | 40.7 | 0.99 | 14.4 |
it can be seen that in all cases a very consistent increase in angular tolerance can be obtained.
It is observed that, in general:
on the one hand, C takes a relatively small value and the ratio with respect to C is very small in all cases; and is
Pupil diameter, in millimeters; c, expressed in diopter; ψ, expressed in degrees, their product is very close to 114.
Thus, in practice, the cylinder power of each sector 10 and 11 is directly denoted by C (i.e. C can be considered to be zero), and the angle ψ is chosen which satisfies the following equation:
the angle psi is expressed in degrees, the cylinder power C in diopters, and the pupil diameter DP in millimeters.
In the case of a lens having a corrective part of the same type as the part 5 shown in fig. 4, the coefficient α is maintained, except that low-pass filtering and the optimization already applied are applied so that the optical path varies similarly to the curve 15i(i is incremented to 10) to obtain the following values for a pupil diameter of 6 mm:
| C(D) | Δφ(°) | Δφ’(°) |
| 3 | 9.4 | 17.5 |
| 2.5 | 11.3 | 21.0 |
| 2 | 14.0 | 26.6 |
| 1.5 | 18.8 | 35.5 |
| 1 | 28.2 | 54.2 |
| C(D) | α0 | α1 | α2 | α3 | α4 | α5 | α6 | α7 | α8 | α9 | α10 |
| 3 | 1.521 | -0.289 | -1.450 | 0.168 | 0 | 0.040 | 0 | 0.019 | 0 | 0.011 | 0 |
| 2.5 | 1.277 | -0.284 | -1.200 | 0.168 | 0 | 0.041 | 0 | 0.019 | 0 | 0.011 | 0 |
| 2 | 1.034 | -0.299 | -0.942 | 0.165 | 0 | 0.048 | 0 | 0.022 | 0 | 0.010 | 0 |
| 1.5 | 0.775 | -0.273 | -0.661 | 0.163 | 0 | 0.040 | 0 | 0.018 | 0 | 0.011 | 0 |
| 1 | 0.522 | -0.261 | -0.383 | 0.157 | 0 | 0.038 | 0 | 0.018 | 0 | 0.010 | 0 |
similarly, for a pupil diameter of 8 mm, the following values can be obtained:
| C(D) | Δφ(°) | Δφ’(°) |
| 3 | 7.2 | 13.3 |
| 2.5 | 8.5 | 16 |
| 2 | 10.6 | 20.1 |
| 1.5 | 14.0 | 26.9 |
| 1 | 21.1 | 40.8 |
| C(D) | α0 | α1 | α2 | α3 | α4 | α5 | α6 | α7 | α8 | α9 | α10 |
| 3 | 1.502 | -0.216 | -1.465 | 0.127 | 0 | 0.031 | 0 | 0.014 | 0 | 0.008 | 0 |
| 2.5 | 1.261 | -0.218 | -1.215 | 0.126 | 0 | 0.030 | 0 | 0.014 | 0 | 0.008 | 0 |
| 2 | 1.015 | -0.214 | -0.964 | 0.127 | 0 | 0.031 | 0 | 0.014 | 0 | 0.008 | 0 |
| 1.5 | 0.766 | -0.212 | -0.695 | 0.124 | 0 | 0.030 | 0 | 0.014 | 0 | 0.008 | 0 |
| 1 | 0.516 | -0.203 | -0.425 | 0.121 | 0 | 0.030 | 0 | 0.014 | 0 | 0.008 | 0 |
note that the increment between delta phi' and delta phi varies between 86 and 92%.
In addition, note that with respect to the coefficient αiIf dividing by α0And alpha2The sum of the squares of the other coefficients varies between 0.095 and 0.119 without calculation. This proves that the introduced power is not purely spherical since, if that is the case, the sum found should be zero.
In this regard, it is shown that if the correction provided is purely spherocylindrical, except for α0And alpha2All but zero coefficients should be; coefficient alpha0Equal to C/2, coefficient α2Equal to-C/2.
In the particular embodiment shown in figures 10-12, the correcting portion 5 is not divided into two sectors by the plane 9, but into four sectors by the plane 9 and by a plane 20 orthogonal to the plane 9, respectively, the sectors 21-24 being differentiated to provide correction of astigmatism whose axis is inclined by an angle ψ in one direction and in the other, alternately with respect to the axis φ. More specifically, the correction of astigmatism is oriented along the axis phi-psi in the opposite sectors 21 and 23 corresponding to a series of points a, which are points at an angle theta-phi between 0 deg. and 90 deg. and between 180 deg. and 270 deg.; whereas the correction of astigmatism is oriented along the axis phi + psi for the opposite sectors 22 and 24 corresponding to a series of points a between 90 deg. and 180 deg. and 270 deg. and 360 deg. of angle theta-phi as shown by the curve 25 in figure 11.
When the same sign as that of the lens whose correcting portion 5 is shown in fig. 4 is used, the optical path introduced by the correcting portion 5 shown in fig. 10 satisfies the following equation:
in the equation, η is equal to ψ when θ - φ is between 0 ° and 90 ° and θ - φ is between 180 ° and 270 °; when theta-phi is between 90 deg. and 180 deg. and theta-phi is between 270 deg. and 360 deg., eta is equal to-psi, and c and psi are constants.
The curve 26 drawn with a solid line in fig. 12 is identical to the curve 13 in fig. 6 and represents the function:
2δtoric/h2
variation as a function of theta-phi
This is the case for cylinder powers of 2 diopters.
The curve 27, drawn with a dashed line, represents a function
2δA(h，θ)/h2
That is to say:
when theta-phi is between 0 deg. and 90 deg. (sector 21) and when theta-phi is between 180 deg. and 270 deg. (sector 23): (C + C) sin2[θ-(φ-ψ)]；
When theta-phi is between 90 deg. and 180 deg. (sector 22) and when theta-phi is between 270 deg. and 360 deg. (sector 24): (C + C) sin2[θ-(φ+ψ)]
c is zero or negligible.
That is, when θ - φ is between 0 ° and 90 ° (sector 21) and when θ - φ is between 180 ° and 270 ° (sector 23), curve 27 is equivalent to curve 26 shifted to the right by the value ψ; while for the other values of theta-phi (sector 22 and sector 24) curve 27 corresponds to curve 13 shifted to the left by the value psi.
More specifically, in this illustrated example, the cylinder power C is 2 diopters, and the values of C and ψ are 0.00 diopters and 7.4 degrees, respectively, for a pupil of 6 millimeters, which is determined by the optimization as described above.
The optical path shown by curve 28 in fig. 13 is obtained by processing the optical path shown by curve 27 in the same way as the optical path shown by curve 15 is obtained from the optical path shown by curve 14, with the coefficient αiThe following values are given:
| α0 | α1 | α2 | α3 | α4 | α5 | α6 | α7 | α8 | α9 | α10 |
| 0.830 | 0 | -0.940 | 0 | 0.112 | 0 | 0 | 0 | 0.023 | 0 | 0 |
in general, it can be seen that curve 28 is quite similar to curve 27, except that, on the one hand, curve 28 does not exhibit a W-shape in the vicinity of θ - φ equal to 0 ° and θ - φ equal to 180 °, but exhibits a simple U-shape corresponding to a smoothed W-shape; and, on the other hand, the maximum values that occur when theta-phi equals 90 deg. and theta-phi equals 270 deg., respectively, are less pronounced than the maximum value in curve 27.
It can be noted that the curves 14 and 15 have a period of 2 pi, while the curves 27 and 28 have a period of pi.
By the optimization processing as shown above, for a lens whose correcting part 5 corresponds to the correcting part shown in fig. 10, when the pupil diameter is 6 mm, the following values can be obtained:
| C(D) | Δφ(°) | Δφ’(°) | C+c(D) | ψ(°) |
| 3 | 9.4 | 13.9 | 2.98 | 5.0 |
| 2.5 | 11.3 | 16.7 | 2.47 | 6.1 |
| 2 | 14.0 | 21.0 | 2.00 | 7.4 |
| 1.5 | 18.8 | 28.4 | 1.47 | 10.5 |
| 1 | 28.2 | 44.2 | 0.95 | 16.7 |
similarly, for a pupil diameter of 8 mm, the following values can be obtained:
| C(D) | Δφ(°) | Δφ’(°) | C+c(D) | ψ(°) |
| 3 | 7.2 | 10.4 | 3.00 | 3.6 |
| 2.5 | 8.5 | 12.6 | 2.48 | 4.5 |
| 2 | 10.6 | 15.9 | 1.98 | 5.7 |
| 1.5 | 14.0 | 21.3 | 1.49 | 7.5 |
| 1 | 21.1 | 32.7 | 0.97 | 12.0 |
it may be noted that the increments within the tolerance range vary between 46 and 55% and that the value of c is still small as indicated in the previous embodiment.
A contact lens having such a path as shown by curve 28, low pass filtered and coefficient optimized, gives the following values for a pupil diameter of 6 mm:
| C(D) | Δφ(°) | Δφ’(°) |
| 3 | 9.4 | 13.7 |
| 2.5 | 11.3 | 16.5 |
| 2 | 14.0 | 20.8 |
| 1.5 | 18.8 | 28.2 |
| 1 | 28.2 | 43.8 |
| C(D) | α0 | α1 | α2 | α3 | α4 | α5 | α6 | α7 | α8 | α9 | α10 |
| 3 | 1.331 | 0 | -1.472 | 0 | 0.114 | 0 | 0 | 0 | 0.023 | 0 | 0 |
| 2.5 | 1.071 | 0 | -1.206 | 0 | 0.107 | 0 | 0 | 0 | 0.024 | 0 | 0 |
| 2 | 1.830 | 0 | -0.940 | 0 | 0.112 | 0 | 0 | 0 | 0.023 | 0 | 0 |
| 1.5 | 0.575 | 0 | -0.667 | 0 | 0.108 | 0 | 0 | 0 | 0.024 | 0 | 0 |
| 1 | 0.332 | 0 | -0.384 | 0 | 0.105 | 0 | 0 | 0 | 0.025 | 0 | 0 |
similarly, for a pupil diameter of 8 mm, the following values can be obtained:
| C(D) | Δφ(°) | Δφ’(°) |
| 3 | 7.2 | 10.4 |
| 2.5 | 8.5 | 12.4 |
| 2 | 10.6 | 15.1 |
| 1.5 | 14.0 | 21.1 |
| 1 | 21.0 | 32.5 |
| C(D) | α0 | α1 | α2 | α3 | α4 | α5 | α6 | α7 | α8 | α9 | α10 |
| 3 | 1.365 | 0 | -1.471 | 0 | 0.081 | 0 | 0 | 0 | 0.016 | 0 | 0 |
| 2.5 | 1.125 | 0 | -1.231 | 0 | 0.085 | 0 | 0 | 0 | 0.017 | 0 | 0 |
| 2 | 1.846 | 0 | -0.951 | 0 | 0.068 | 0 | 0 | 0 | 0.017 | 0 | 0 |
| 1.5 | 0.593 | 0 | -0.693 | 0 | 0.062 | 0 | 0 | 0 | 0.017 | 0 | 0 |
| 1 | 0.358 | 0 | -0.424 | 0 | 0.076 | 0 | 0 | 0 | 0.017 | 0 | 0 |
it can be seen that the parameter α is other than when i ═ 0 and i ═ 2iThe sum of squares of (a) is 0.007 each time.
The improvement in tolerance with respect to angular displacement is between 41 and 53%.
According to the lens of this second embodiment, it is thereby obtained that the angular displacement tolerance range is not significantly enlarged. It is noted, however, that this arrangement in this embodiment shows a very good tolerance of defects in the centre, i.e. the coincidence between the optical axis 2 of the lens and the visual axis of the eye, due to the relative arrangement of the sectors, the inclination of which relative to the correction axis of the sectors is the same.
For the corrective part 5 as shown in fig. 4, it can be generally seen that:
on the one hand, C takes a relatively small value, the ratio of which in any case relative to C is small; and is
Pupil diameter, in millimeters; c, expressed in diopter; ψ, expressed in degrees, the product of these three is always very close to 90.
In practice, C can be used directly as the cylinder power for each sector 21-24 (i.e. C equals zero) and ψ is chosen which satisfies the following equation:
the angle psi is expressed in degrees, the cylinder power C in diopters, and the pupil diameter DP in millimeters.
In the corrective part 5 shown in fig. 4 and 10, respectively, the angle ψ is positive, but it is also not objected that ψ takes a negative value.
In other variants of the correction part 5, not shown, the number of sectors may be different from two or four and/or the number of axes and/or cylinders in each sector may be different.
It is noted that in addition to the coefficient α detailed above0And alpha2Besides, the coefficients α representing the continuous component and the periodic π component, respectively0And alpha2With respect to the coefficient αi：
In all cases, the coefficient α increases with iiRapidly reduced to very small;
for the case of the curve 15 (fig. 7), starting from i-4, all the even-term coefficients are equal to zero, and the coefficient α9Are all close to 0.01; and
for the case of the curve 28 (fig. 13), if the coefficient α is removed0And alpha2Only coefficient α4And alpha8Is not zero.
In general, the optical path δ introduced by a lens according to the inventionA(h, θ), and in particular the optical paths shown by curves 14, 15, 27, 28, can be expressed in the form:
δA(h，θ)＝δtoric(h ，θ)+δatoric(h，θ)
δatoric(h, theta) is a function that varies as a function of theta with a period of 2, which is comparable to sin, when h is constant2(theta-phi) are different.
In the case of the optical paths 14 and 27, δatoric(h, θ) is the optical path δAA non-toric component of (h, θ) corresponding to a difference between the optical paths represented by the curve 14 and the curve 13, respectively; and corresponds to the difference from the optical paths represented by the curve 27 and the curve 26, respectively.
In the case of the optical paths, δ, as shown by curves 15 and 18, respectivelyatoric(h, θ) are represented by curves 29 and 29 in FIG. 14, respectivelyAs represented by curve 30.
More specifically, these curves are all formed by the above-mentioned coefficient α1And alpha3To alpha10Given, i.e. by removing a0And alpha2Coefficient set alpha ofiGiven below.
It is to be noted that the curve 29 is very close to the difference between the curves 13 and 15, however, not equal to this difference, since α01.034 (not C/2 or 2/2 ═ 1.00 diopters), and α2At-0.942 (not-C/2 or-1.000), the toric component δ of the optical path shown in curve 15toric(h, θ) is not exactly equal to the optical path shown by curve 13.
The same can be observed for curve 30, since α0＝0.830，α2Plot 30 does not correspond to the difference between plot 26 and plot 28, which is-0.940.
It is to be noted that the curve 29 has a period of 2 pi, the portions of the curve 29 lying between 0 and pi (180 deg.) and pi and 2 pi (360 deg.), respectively, being symmetrical, i.e. one being a mirror image of the other.
Curve 29 decreases approximately to 45 °; it increases to about θ - Φ -135 °; then reducing to a position where theta-phi is 180 degrees; increasing to theta-phi of 225 deg.; decreases to 315 deg., and then increases to 360 deg..
The curve 30 has a period pi/2 that decreases from 0 deg. to 45 deg. and then increases to 90 deg..
For a pupil diameter of 8 mm, curves are obtained which vary in the same manner as curves 29 and 30, respectively, but with a smaller magnitude.
With regard to the values given so far, it should be noted that:
for a corrective part 5 of the type shown in figures 4 and 10, a better result is obtained until the value of C + C is shifted by ± 0.125 diopters, and ψ is shifted by ± 1 °;
for the corrective part introduced into the type of optical path shown in figures 7 and 13, the parameter α given aboveiDeviations can occur as long as the deviation distance, as indicated by the mathematical term, remains less than 0.05, that is as long as:
coefficient α in this equationiIs a coefficient (with tolerance) that exists in practice, the coefficient alphai' are nominal coefficients, i.e. those given in the tables appearing in the previous description with reference to the figures.
In a specific embodiment not shown, the optical path is again varied as a function of h.
In a first embodiment of this type, the optical path introduced by the lens correction portion is written in the form:
in this equation:
e is a finite set of integers starting from 0; and
βi(h) is a set of functions that satisfy the following equations:
j is an integer that varies as a function of h by segment; alpha is alphai，jIt is a predetermined constant coefficient regardless of i and j.
The cylinder power is a function of h in the region corresponding to each stage, and is also a constant when θ is constant.
In another example of the above type, βi(h) Is a set of functions that satisfy the following equations:
m in this equation is a predetermined integer, each αijIs a predetermined constant coefficient independent of i and j.
The cylinder power varies slowly as a function of h as a polynomial function when theta is constant.
Since the shape of the rear surface 4 is known (spherical in this embodiment) and the refractive index of the lens material is also known, the coordinates of the different points a on the front surface 3 can be determined by known methods from the optical path δ (h, θ) chosen so that h is at least 0.4 mm to 2.4 mm, satisfying the equation:
δ(h，θ)＝δ0+δA(h，θ)
in this equation, δ0Is an arbitrary constant, δA(h, θ) have the above tolerance.
The optical path thus defined enables to determine a shape suitable for the front surface of the correcting portion 5.
In a variant of the lens 1, its rear surface 4 is replaced by an aspherical shape, originally purely spherical, which is mechanically adapted to the geometry of the cornea of the eye intended to receive the lens, in fact it is selected from a series of predetermined shapes obtained by testing the eye intended to be worn.
For another deformation of the lens 1, the shape of the front surface 3 is selected from a series of known surfaces, the shape of which matches the determined rear surface 4.
In other variants not shown, the lightening portions 6 and 7 are replaced by other different means for centring and rotational stabilization, in particular by a kinematic flange as disclosed in french patent No.2760853, or by the lower placement of a ballast prism, also done by lightening portions in the top.
In another embodiment, the lens according to the invention is used for correcting, in addition to astigmatism, also progressive simultaneous vision correction for myopia or hyperopia and/or presbyopia.
The above-mentioned optical path δ (h, θ) fully satisfies the inequality:
δinf(h，θ)≤δ(h，θ)≤δsup(h，θ)
where delta isinf(h, theta) and deltasup(h，θ) satisfy the following equations, respectively:
δinf(h，θ)＝δ0+δs(h)+δp(h)+δA(h，θ)-0.09h2
δsup(h，θ)＝δinf(h，θ)+0.18h2
in this equation, h and all δ are expressed in meters (m):
in the case of spherical correction, s (h) is the optical path used to perform this correction, which satisfies the equation:
in this equation, PVLIs the sphere power required to correct myopia or hyperopia of the eye, expressed in diopters (D);
delta in the case of progressive simultaneous vision correctionP(h) Is the optical path for this correction, which satisfies the equation:
a series of systems gamma2kAre determined by one of the nine coefficient lists SA, SB, SC, MA, MB, MC, LA, LB, LC, respectively, given below:
| k | SA | SB | SC |
| 0 | 1.398800E+00 | 3.093330E+00 | 4.605640E+00 |
| 1 | -2.160020E+00 | -4.751140E+00 | -5.235240E+00 |
| 2 | 1.337720E+00 | 2.913640E+00 | 2.458240E+00 |
| 3 | -4.327890E-01 | -9.378340E-01 | -6.301520E-01 |
| 4 | 8.154230E-02 | 1.764900E-01 | 9.787570E-02 |
| 5 | -9.410290E-03 | -2.038990E-02 | -9.616130E-03 |
| 6 | 6.736380E-04 | 1.462890E-03 | 6.012020E-04 |
| 7 | -2.914960E-05 | -6.347570E-05 | -2.318560E-05 |
| 8 | 6.978470E-07 | 1.520000E-06 | 5.030000E-07 |
| 9 | -7.091930E-09 | -1.550000E-08 | -4.690000E-09 |
| k | MA | MB | MC |
| 0 | 1.799020E+00 | 3.048790E+00 | 4.144890E+00 |
| 1 | -1.823880E+00 | -3.424400E+00 | -4.233760E+00 |
| 2 | 8.133470E-01 | 1.714210E+00 | 1.949870E+00 |
| 3 | -2.057150E-01 | -4.850380E-01 | -5.212190E-01 |
| 4 | 3.222470E-02 | 8.400400E-02 | 8.739800E-02 |
| 5 | -3.231690E-03 | -9.184070E-03 | -9.410210E-03 |
| 6 | 2.075120E-04 | 6.343800E-04 | 6.468110E-04 |
| 7 | -8.241900E-06 | -2.679260E-05 | -2.734250E-05 |
| 8 | 1.842050E-07 | 6.310000E-07 | 6.460000E-07 |
| 9 | -1.770040E-09 | -6.330000E-09 | -6.520000E-09 |
| k | LA | LB | LC |
| 0 | 1.258120E+00 | 2.3409009E+00 | 2.660000E+00 |
| 1 | 2.766510E-01 | -1.6016233E+00 | -3.029760E+00 |
| 2 | -5.863900E-01 | 8.5580090E-01 | 1.837520E+00 |
| 3 | 2.158210E-01 | -4.0855924E-01 | -6.361990E-01 |
| 4 | -3.890640E-02 | 1.2233248E-01 | 1.293960E-01 |
| 5 | 4.063430E-03 | -2.1406740E-02 | -1.595350E-02 |
| 6 | -2.578890E-04 | 2.2148862E-03 | 1.205290E-03 |
| 7 | 9.821560E-06 | -1.3380186E-04 | -5.450000E-05 |
| 8 | -2.065710E-07 | 4.3658573E-06 | 1.350000E-06 |
| 9 | 1.845210E-09 | -5.9468409E-08 | -1.410000E-08 |
(E and the following values represent powers of 10).
In a variant of this embodiment, for the correction of presbyopia, instead of using a central part of the correcting portion 5 having a higher refractive power than the periphery as above, a change in the opposite direction is used, i.e. the refractive power at the central part of the correcting portion is lower than the refractive power at the periphery.
In this case, the optical path introduced by the progressive simultaneous vision correction is no longer given above, but:
PADDis the add power, expressed in diopters (D), required by the lens wearer for near vision2kThe set is determined by one of the nine lists SA, SB, SC, MA, MB, MC, LA, LB, LC, respectively, given above.
In a variant which is not shown, a correction part, such as part 5, is obviously not a contact lens but an intraocular lens in the form of an implant.
Many other variations may be made in accordance with this situation, and it is reiterated in this regard that the present invention is not limited to the illustrated and described embodiments.
Claims (39)
1. A contact lens comprising a correcting portion (5) for correcting the vision of an eye which may be myopic or hyperopic and/or may be presbyopic astigmatic, comprising an optical axis (2) and a reference meridian (8); the method is characterized in that: for purely astigmatic correction, the variation of the optical path it introduces is a function of the distance (h) from the optical axis (2) and of the angular separation (θ) from the reference meridian (8), according to the following equation, at least when said distance is between 0.4 mm and 2.4 mm:
δA(h，θ)＝δtoric(h，θ)+δatoric(h，θ)
in this equation:
-δtoric(h, theta) is a lenticular first optical path (13, 26) which satisfies the expression delta according to a parabolic approximation methodtoric(h，θ)＝C/2h2sin2(θ - φ), where φ is the axis required to correct astigmatism of the eye, expressed as the angular separation relative to the reference meridian, where C is the cylinder power required to correct astigmatism of the eye and
-δatoric(h, theta) is the second optical path (29, 30) such that when h is constant, its variation is a function of theta with a period of 2 pi, and sin2(different in theta-phi, the optical path additionally satisfies the condition:
Δφ’≥1.3Δφ
in this inequality:
- Δ φ is the amplitude of the variation range [ -1/2 Δ φ, 1/2 Δ φ ] of the variable x, the amplitude being such that for any value of x within the interval the following condition is verified:
- Δ φ ' is the amplitude of the range of variation of the variable x [ -1/2 Δ φ ', 1/2 Δ φ ' ] such that for any value of x within this interval, the following condition is verified:
the notation MTFa [ f (h, θ) ] indicates, for the optical path f (h, θ), the optical performance criterion calculated from the modulation transfer function generated by the optical path, for a predetermined pupil diameter between 4 mm and 7 mm according to the following formula:
in this formula, ν and χ are polar coordinates in the plane of the angular spatial frequency, expressed in cycles per degree, and χ in degrees; wherein the MTF [ f (h, θ) ] (ν, χ) is a modulation transfer function of the optical path f (h, θ) according to said polar coordinates.
2. The lens of claim 1, wherein the term δA(h, θ) satisfies the equation:
in this equation:
-N is a set of integers; and
-βi(h) is a set of functions that satisfy the following conditions:
in the inequality, N' is equal to N except 0 and 2, and hminAnd hmaxRespectively, the minimum and maximum distances with respect to an optical axis (2), the optical axis (2) being the optical axis of a zone of the correction portion (5) for correcting astigmatism.
3. Lens according to claim 2, characterized in that each function β isi(h) Satisfies the equation:
in this equation, α for i ∈ N, αiAre all constant coefficients.
4. Lens according to claim 3, characterized in that the light path δA(h, θ) satisfies the equation:
in this equation, η is equal to Ψ when θ - Φ is between 0 ° and 180 °, and η is equal to Ψ when θ - Φ is between 180 ° and 360 °, and c and Ψ are predetermined constants.
5. Lens according to claim 4, characterized in that the constants C and the value of Ψ depending on the value of C are given by the following table, with accuracy to ± 0.125 diopter (D) for C + C and to ± 1 ° for Ψ:
C(D)
C+c(D)
Ψ
3
3.00
6.3°
2.5
2.48
7.6°
2
2.04
9.1°
1.5
1.49
12.7°
1
1.00
19.1°
6. lens according to claim 4, characterized in that the constants C and the value of Ψ depending on the value of C are given by the following table, with accuracy to ± 0.125 diopter (D) for C + C and to ± 1 ° for Ψ:
C(D)
C+c(D)
Ψ
3
2.99
4.7°
2.5
2.50
5.7°
2
1.98
7.2°
1.5
1.49
9.5°
1
0.99
14.4°
7. lens according to claim 4, characterized in that the constant c is equal to zero and the constant Ψ has a value, given by the following formula, accurate to ± 1 °:
in this formula, DP is the pupil diameter, expressed in millimeters (mm), Ψ in degrees (°), and C in diopters (D).
8. Lens according to claim 3, characterized in that the light path δA(h, theta) satisfiesThe equation:
in this equation, η is equal to Ψ when θ - φ is between 0 ° and 90 ° and θ - φ is between 180 ° and 270 °; when theta-phi is between 90 deg. and 180 deg. and theta-phi is between 270 deg. and 360 deg., eta is equal to-psi, and c and psi are predetermined constants.
9. Lens according to claim 8, characterized in that the constants C depending on the value of C and the value of Ψ are given by the following table, with accuracy to ± 0.125 diopter (D) for C + C and to ± 1 ° for Ψ:
C(D)
C+c(D)
Ψ(°)
3
2.98
5.0
2.5
2.47
6.1
2
2.00
7.4
1.5
1.47
10.5
1
0.95
16.7
10. lens according to claim 8, characterized in that the constants C depending on the value of C and the value of Ψ are given by the following table, with accuracy to ± 0.125 diopter (D) for C + C and to ± 1 ° for Ψ:
C(D)
C+c(D)
Ψ(°)
3
3.00
3.6
2.5
2.48
4.5
2
1.98
5.7
1.5
1.49
7.5
1
0.97
12.0
11. lens according to claim 8, characterized in that the constant c is equal to zero and the constant Ψ has a value, given by the following formula, accurate to ± 1 °:
in this formula, DP is the pupil diameter, expressed in millimeters (mm), Ψ in degrees (°), and C in diopters (D).
12. The lens of claim 1, wherein the term δA(h, θ) satisfies the equation:
in this equation:
e is a finite set comprising integers starting from 0; and
βi(h) is a set of functions that satisfy the following conditions:
in this inequality, E' is equal to E, h except for 0 and 2minAnd hmaxRespectively, the minimum and maximum distances with respect to an optical axis (2), the optical axis (2) being the optical axis (2) of a zone of the correction portion (5) for correcting astigmatism.
13. The lens according to claim 12,
function betai(h) Each of which satisfies the equation:
in this equation, for iE.g. E, each αiIs a constant coefficient.
14. The lens of claim 13, wherein set E comprises integers from 0 to 10; and coefficient alphaiAs a function of C, its value satisfies the inequality:
coefficient alpha1The values of are given by the following table: C(D) α0` α1` α2` α3` α4` α5` α6` α7` α8` α9` α10`
3
1.521
-0.289
-1.450
0.168
0
0.040
0
0.019
0
0.011
0
2.5
1.277
-0.284
-1.200
0.168
0
0.041
0
0.019
0
0.011
0
2
1.034
-0.299
-0.942
0.165
0
0.048
0
0.022
0
0.010
0
1.5
0.775
-0.273
-0.661
0.163
0
0.040
0
0.018
0
0.011
0
1
0.522
-0.261
-0.383
0.157
0
0.038
0
0.018
0
0.010
0
15. the lens of claim 13, wherein set E comprises integers from 0 to 10; and coefficient alphaiAs a function of C, its value satisfies the inequality:
coefficient alphaiThe values of are given by the following table:
C(D)
α0
α1
α2
α3
α4
α5
α6
α7
α8
α9
α10
3
1.502
-0.216
-1.465
0.127
0
0.031
0
0.014
0
0.008
0
2.5
1.261
-0.218
-1.215
0.126
0
0.030
0
0.014
0
0.008
0
2
1.015
-0.214
-0.964
0.127
0
0.031
0
0.014
0
0.008
0
1.5
0.766
-0.212
-0.695
0.124
0
0.030
0
0.014
0
0.008
0
1
0.516
-0.203
-0.425
0.121
0
0.030
0
0.014
0
0.008
0
16. the lens of claim 13, wherein set E comprises integers from 0 to 10; and coefficient alphaiAs a function of C, its value satisfies the inequality:
coefficient alphaiThe values of are given by the following table:
C(D)
α0
α1
α2
α3
α4
α5
α6
α7
α8
α9
α10
3
1.331
0
-1.472
0
0.114
0
0
0
0.023
0
0
2.5
1.071
0
-1.206
0
0.107
0
0
0
0.024
0
0
2
1.830
0
-0.940
0
0.112
0
0
0
0.023
0
0
1.5
0.575
0
-0.667
0
0.108
0
0
0
0.024
0
0
1
0.332
0
-0.384
0
0.105
0
0
0
0.025
0
0
17. the lens of claim 13, wherein set E comprises integers from 0 to 10; and coefficient alphaiAs a function of C, its value satisfies the inequality:
coefficient of performanceαiThe values of are given by the following table:
C(D)
α0
α1
α2
α3
α4
α5
α6
α7
α8
α9
α10
3
1.365
0
-1.471
0
0.081
0
0
0
0.016
0
0
2.5
1.125
0
-1.231
0
0.085
0
0
0
0.017
0
0
2
1.846
0
-0.951
0
0.068
0
0
0
0.017
0
0
1.5
0.593
0
-0.693
0
0.062
0
0
0
0.017
0
0
1
0.358
0
-0.424
0
0.076
0
0
0
0.017
0
0
18. lens according to claim 12, characterized in that each function β isi(h) All satisfy the equation:
in this equation, j is an integer that is segmented into a functional variation of h; each α is independent of the value of i and jijIs a predetermined constant coefficient.
19. Lens according to claim 12, characterized in that each function β isi(h) All satisfy the equation:
in this equation, M is a predetermined integer; and each alpha is no matter what value i and j takeijIs a predetermined constant coefficient.
20. The lens according to any of claims 1-19, characterized in that the optical path δ (h, θ) introduced by said lens amounts to, at least for h between 0.4 mm and 2.4 mm, the equation:
δ(h，θ)＝δ0+δA(h，θ)
in this equation, δ0Is an arbitrary constant.
21. The lens according to any of claims 1-19, characterized in that the optical path δ (h, θ) introduced by said lens amounts to, at least for h between 0.4 mm and 2.4 mm, the inequality:
δinf(h，θ)≤δ(h，θ)≤δsup(h，θ)
δint(h, theta) and deltasup(h, θ) satisfy the following equations, respectively:
δinf(h，θ)＝δ0+δs(h)+δp(h)+δA(h，θ)-0.09h2
δsup(h，θ)＝δinf(h，θ)+0.18h2
in this equation, h and all δ are expressed in meters (m):
in the case of spherical correction, δ s (h) is the optical path used to perform this correction, which satisfies the equation:
in this equation, PVLIs the required spherical power, expressed in diopters (D), to correct either myopia or hyperopia of the eye;
delta in the case of progressive simultaneous vision correctionP(h) Is the optical path used to perform the correction, which satisfies the equation:
coefficient gamma2kThe series is determined by one of the nine coefficient lists SA, SB, SC, MA MB, MC, LA, LB, LC, respectively, given below:
K
SA
SB
SC
0
1.398800E+00
3.093330E+00
4.605640E+00
1
-2.160020E+00
-4.751140E+00
-5.235240E+00
2
1.337720E+00
2.913640E+00
2.458240E+00
3
-4.327890E-01
-9.378340E-01
-6.301520E-01
4
8.154230E-02
1.764900E-01
9.787570E-02
5
-9.410290E-03
-2.038990E-02
-9.616130E-03
6
6.736380E-04
1.462890E-03
6.012020E-04
7
-2.914960E-05
-6.347570E-05
-2.318560E-05
8
6.978470E-07
1.520000E-06
5.030000E-07
9
-7.091930E-09
-1.550000E-08
-4.690000E-09
K
MA
MB
MC
0
1.799020E+00
3.048790E+00
4.144890E+00
1
-1.823880E+00
-3.424400E+00
-4.233760E+00
2
8.133470E-01
1.714210E+00
1.949870E+00
3
-2.057150E-01
-4.850380E-01
-5.212190E-01
4
3.222470E-02
8.400400E-02
8.739800E-02
5
-3.231690E-03
-9.184070E-03
-9.410210E-03
6
2.075120E-04
6.343800E-04
6.468110E-04
7
-8.241900E-06
-2.679260E-05
-2.734250E-05
8
1.842050E-07
6.310000E-07
6.460000E-07
9
-1.770040E-09
-6.330000E-09
-6.520000E-09
K
LA
LB
LC
0
1.258120E+00
2.3409009E+00
2.660000E+00
1
2.766510E-01
-1.6016233E+00
-3.029760E+00
2
-5.863900E-01
8.5580090E-01
1.837520E+00
3
2.158210E-01
-4.0855924E-01
-6.361990E-01
4
-3.890640E-02
1.2233248E-01
1.293960E-01
5
4.063430E-03
-2.1406740E-02
-1.595350E-02
6
-2.578890E-04
2.2148862E-03
1.205290E-03
7
9.821560E-06
-1.3380186E-04
-5.450000E-05
8
-2.065710E-07
4.3658573E-06
1.350000E-06
9
1.845210E-09
-5.9468409E-08
-1.410000E-08
22. the lens according to any of claims 1 to 19, characterized in that the optical path δ (h, θ) introduced by said lens amounts to, at least for h lying between 0.4 mm and 2.4 mm, the inequality:
δinf(h，θ)≤δ(h，θ)≤δsup(h，θ)
δint(h, theta) and deltasup(h, θ) satisfy the following equations, respectively:
δsinf(h，θ)＝δ0+δs(h)+δp(h)+δA(h，θ)-0.09h2
δsup(h，θ)＝δinf(h，θ)+0.18h2
in this equation, h and all δ are expressed in meters (m):
in the case of spherical correction, δ s (h) is the optical path used to perform this correction, which satisfies the equation:
in this equation, PVLIs the spherical power required to correct the myopia or hyperopia of said eye, expressed in diopters (D);
delta in the case of progressive simultaneous vision correctionP(h) Is the optical path used to make this correction, which satisfies the equation:
where P isADDIs the add power, expressed in diopters (D), required by the lens wearer for near vision2kThe sets are determined by one of the nine coefficient lists SA, SB, SC, MA, MB, MC, LA, LB, LC, respectively, given below:
k
SA
SB
SC
0
1.398800E+00
3.093330E+00
4.605640E+00
1
-2.160020E+00
-4.751140E+00
-5.235240E+00
2
1.337720E+00
2.913640E+00
2.458240E+00
3
-4.327890E-01
-9.378340E-01
-6.301520E-01
4
8.154230E-02
1.764900E-01
9.787570E-02
5
-9.410290E-03
-2.038990E-02
-9.616130E-03
6
6.736380E-04
1.462890E-03
6.012020E-04
7
-2.914960E-05
-6.347570E-05
-2.318560E-05
8
6.978470E-07
1.520000E-06
5.030000E-07
9
-7.091930E-09
-1.550000E-08
-4.690000E-09
k
MA
MB
MC
0
1.799020E+00
3.048790E+00
4.144890E+00
1
-1.823880E+00
-3.424400E+00
-4.233760E+00
2
8.133470E-01
1.714210E+00
1.949870E+00
3
-2.057150E-01
-4.850380E-01
-5.212190E-01
4
3.222470E-02
8.400400E-02
8.739800E-02
5
-3.231690E-03
-9.184070E-03
-9.410210E-03
6
2.075120E-04
6.343800E-04
6.468110E-04
7
-8.241900E-06
-2.679260E-05
-2.734250E-05
8
1.842050E-07
6.310000E-07
6.460000E-07
9
-1.770040E-09
-6.330000E-09
-6.520000E-09
k
LA
LB
LC
0
1.258120E+00
2.3409009E+00
2.660000E+00
1
2.766510E-01
-1.6016233E+00
-3.029760E+00
2
-5.863900E-01
8.5580090E-01
1.837520E+00
3
2.158210E-01
-4.0855924E-01
-6.361990E-01
4
-3.890640E-02
1.2233248E-01
1.293960E-01
5
4.063430E-03
-2.1406740E-02
-1.595350E-02
6
-2.578890E-04
2.2148862E-03
1.205290E-03
7
9.821560E-06
-1.3380186E-04
-5.450000E-05
8
-2.065710E-07
4.3658573E-06
1.350000E-06
9
1.845210E-09
-5.9468409E-08
-1.410000E-08
23. a contact lens comprising a portion for correcting astigmatic eye vision, the lens defining an optical axis and a reference meridian perpendicular to the optical axis; the lens further having a generally convex anterior surface and a generally concave posterior surface, wherein one of the anterior or posterior surfaces has a shape capable of correcting astigmatism, and wherein the variation of the optical path through said correcting portion of the lens is a function of the angular separation from the reference meridian; wherein the correction portion is divided into at least two sectors having different astigmatic correction axes, the lens being configured to have an increased angular misalignment tolerance of at least about 30% relative to a standard toric lens of the same class.
24. The lens of claim 23 wherein the correcting portion is defined within a circle about the optical axis having a radius of 0.4 mm to 2.4 mm.
25. The lens of claim 23 wherein said two sectors are separated by a line passing through the optical axis, said sectors being angularly oriented at an angle phi relative to a reference meridian, which is the nominal axis required to correct astigmatism of said eye.
26. The lens of claim 25 wherein the two sectors each have an astigmatism correction axis different from Φ.
27. The lens of claim 26, wherein one of said two sectors has an astigmatism correction axis equal to phi-psi and the other of said two sectors has an astigmatism correction axis equal to phi + psi, where psi is non-zero.
28. The lens of claim 23 wherein the correcting portion is divided into four sectors, at least two of which have different axes of astigmatic correction.
29. The lens of claim 28, wherein the four sectors are separated by two perpendicular lines intersecting at an optical axis, thereby defining two pairs of diametrically opposed sectors across the optical axis, wherein the angular orientation of a line with respect to a reference meridian is an angle Φ.
30. The lens of claim 29 wherein each pair of diametrically opposed sectors across the optical axis have equal astigmatism correction axes.
31. The lens of claim 30, wherein two of said sectors have an astigmatism correction axis equal to phi-psi and two other of said sectors have an astigmatism correction axis equal to phi + psi, where psi is non-zero.
32. A contact lens comprising a portion for correcting astigmatic eye vision, the lens having an anterior surface and a posterior surface and defining an optical axis and a reference meridian perpendicular to the optical axis, characterized in that at least one of the anterior or posterior surfaces has a non-axisymmetric shape that is not purely toric; wherein the distribution of the optical paths through said correcting part of the lens is the sum of a plurality of optical paths including at least:
an optical path describing astigmatic correction characteristics; and
optical paths describing non-axisymmetric aberration characteristics other than astigmatism,
the lens is configured to have an increased angular misalignment tolerance of at least about 30% relative to a standard toric lens of the same class.
33. The lens of claim 32, wherein only the anterior surface is non-axisymmetric.
34. The lens of claim 32, wherein only the back surface is non-axisymmetric.
35. The lens of claim 32, wherein the anterior and posterior surfaces are both non-axisymmetric.
36. The lens of claim 32, wherein the optical path through the correcting portion of the lens further corrects for spherical errors.
37. The lens of claim 32, wherein the optical path through the corrective portion of the lens further includes a correction for presbyopia multifocal.
38. The lens of claim 32, wherein the optical path through the correcting portion of the lens further comprises a progressive power correction for presbyopia.
39. The lens of claim 32, wherein the optical path through the correcting portion of the lens further corrects for coma.
Applications Claiming Priority (3)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US09/910,491 US6533416B1 (en) | 2001-07-20 | 2001-07-20 | Contact or intraocular lens and method for its preparation |
| US09/910,491 | 2001-07-20 | ||
| PCT/US2002/022808 WO2003009053A1 (en) | 2001-07-20 | 2002-07-18 | Contact or intraocular lens and method for its preparation |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| HK1069880A1 HK1069880A1 (en) | 2005-06-03 |
| HK1069880B true HK1069880B (en) | 2007-05-04 |
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ID=
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